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6.58M
Aesthetics
Feng shui
https://en.wikipedia.org/wiki/Feng_shui
What is another name for feng shui?
Chinese geomancy
What does 'feng shui' literally mean?
Wind-water
Where did feng shui originate?
Ancient China
What does feng shui claim to do?
Harmonize individuals with environment
How have scientists and philosophers classified feng shui?
Non-scientific and pseudoscientific
Discuss feng shui by addressing: (1) its alternate name, (2) its literal meaning, (3) its origin, (4) its claimed purpose, and (5) its classification by experts.
Give a brief overview of feng shui.
Feng shui is known as Chinese geomancy, literally means wind-water, originated in Ancient China, claims to harmonize individuals with their environment, and is classified as non-scientific and pseudoscientific."
307,628
Aesthetics
Fashion
https://en.wikipedia.org/wiki/Fashion
What Latin word is the origin of 'fashion'?
Facere
In what year does the French word 'mode' date back to?
1482
From which century is the English term for 'in style' derived?
16th century
What urgent issue emerged in fashion due to mass production?
Reducing environmental impact and improving sustainability
Which fashion scholar stated everyone is 'forced to appear'?
Susan B. Kaiser
Discuss fashion by addressing: (1) its Latin origin, (2) the dating of the French word 'mode', (3) the century of the English term for 'in style', (4) the emerging issue from mass production, and (5) the scholar who stated that everyone is 'forced to appear'.
Summarize the key origins and sustainability concerns in fashion.
Fashion originates from 'Facere'. The French term dates back to 1482 and the English term arose in the 16th century. The industry now focuses on reducing environmental impact and improving sustainability, as stated by Susan B. Kaiser."
289,637
Aesthetics
Modernism
https://en.wikipedia.org/wiki/Modernism
When was Pablo Picasso's Les Demoiselles d'Avignon created?
1907
Who designed the Bauhaus building?
Walter Gropius
What did modernism emphasize in literature, visual arts, and music?
Experimentation, abstraction, and subjective experience
What belief did modernism center around regarding prevailing values?
Growing alienation from prevailing morality, optimism, and convention
After which war did cultural and geopolitical shifts influence modernism?
World War I
Discuss modernism by addressing: (1) when Pablo Picasso's Les Demoiselles d'Avignon was created, (2) who designed the Bauhaus building, (3) what modernism emphasized in literature, visual arts, and music, (4) what belief modernism centered around regarding prevailing values, and (5) after which war cultural and geopolitical shifts influenced it
Summarize the key aspects of modernism
Les Demoiselles d'Avignon was created in 1907, and Walter Gropius designed the Bauhaus building; modernism emphasized experimentation, abstraction, and subjective experience while embracing growing alienation from prevailing morality, optimism, and convention, and it was influenced by the aftermath of World War I."
281,674
Aesthetics
Aesthetics
https://en.wikipedia.org/wiki/Aesthetics
What branch of philosophy is concerned with the nature of beauty and taste?
Aesthetics
From which language is the word 'aesthetic' derived?
Ancient Greek
Who wrote the series 'The Pleasures of the Imagination'?
Joseph Addison
Who coined the term 'aesthetics' with its new meaning in 1735?
Alexander Baumgarten
What is the function of aesthetics?
Critical reflection on art, culture and nature
Discuss aesthetics by addressing: (1) which branch of philosophy is concerned with the nature of beauty and taste, (2) from which language the word 'aesthetic' is derived, (3) who wrote the series 'The Pleasures of the Imagination', (4) who coined the term 'aesthetics' with its new meaning in 1735, and (5) what is the function of aesthetics?
Summarize the key aspects of aesthetics
Aesthetics, derived from Ancient Greek, was shaped by Joseph Addison and Alexander Baumgarten, ultimately serving as critical reflection on art, culture and nature"
277,790
Aesthetics
Poetry
https://en.wikipedia.org/wiki/Poetry
What does the term 'poetry' originate from?
Greek word 'poiesis' meaning 'making'
What is an individual work of poetry called?
A poem
Which poetic device imitates natural sounds?
Onomatopoeia
What term has become a synonym for poetry due to its written format?
Verse
Which poetry tradition is noted for its unique use of alliteration and metre independent of writing?
Somali poetry
Discuss poetry by addressing: (1) What does the term 'poetry' originate from?, (2) What is an individual work of poetry called?, (3) Which poetic device imitates natural sounds?, (4) What term has become a synonym for poetry due to its written format?, (5) Which poetry tradition is noted for its unique use of alliteration and metre independent of writing?
Provide a brief overview of poetry.
Poetry derives its name from the Greek word 'poiesis' meaning 'making'; an individual work is called a poem; onomatopoeia serves as a sound device; written works are formatted as verse; and Somali poetry highlights a distinct tradition."
251,415
Aesthetics
Design
https://en.wikipedia.org/wiki/Design
What is the name of the wall clock designed by Dieter Rams and Dietrich Lubs in the early 1980s?
Braun ABW30 wall clock
Who designed the cutlery for the Victorinox Swiss Army knife in 2007?
Zaha Hadid
Which architect produced early concept design sketches exploring building relationships?
Erling Viksjø
Who is considered the father of safe driving and safety tests?
Barényi Béla
What are people who produce designs called?
Designers
Discuss design contributions by addressing: (1) the name of the wall clock designed by Dieter Rams and Dietrich Lubs in the early 1980s, (2) the designer of Victorinox Swiss Army knife cutlery in 2007, (3) the architect behind early concept design sketches exploring building relationships, (4) the individual regarded as the father of safe driving and safety tests, and (5) the term for people who produce designs
Summarize key design examples and contributors
The Braun ABW30 wall clock, Zaha Hadid, Erling Viksjø, and Barényi Béla collectively highlight distinct facets of design, representing the creative work of designers"
228,538
Aesthetics
Artist
https://en.wikipedia.org/wiki/Artist
What is the most common usage of the term 'artist'?
Practitioner in the visual arts
Which French variant of 'artist' is rarely used in English?
Artiste
Which term is generally used instead of 'artist' for writers?
Author
Who painted 'Goethe in the Roman Campagna'?
Johann Heinrich Wilhelm Tischbein
What does the Greek word technÄ› imply?
Mastery of any craft
Discuss the term 'artist' by addressing: (1) what is the most common usage of the term 'artist', (2) which French variant is rarely used in English, (3) which term is generally used instead of 'artist' for writers, (4) who painted 'Goethe in the Roman Campagna', and (5) what does the Greek word technÄ› imply?
Summarize the key aspects of the term 'artist'
An artist is primarily a practitioner in the visual arts, with the term artiste used rarely and author preferred for writers; additionally, Johann Heinrich Wilhelm Tischbein exemplifies artistic heritage while technÄ› implies mastery of any craft"
135,040
Aesthetics
Masterpiece
https://en.wikipedia.org/wiki/Masterpiece
Which painting by Leonardo da Vinci is considered an archetypal masterpiece?
Mona Lisa
In what year was the term 'masterpiece' first recorded outside a guild context?
1605
What is the early variant of the term 'masterpiece'?
Masterprize
Which literary work is regarded as a masterpiece of Nigerian literature?
Things Fall Apart
What did apprentices produce to qualify as masters in the guild system?
A masterpiece
Discuss the concept of a masterpiece by addressing: (1) which painting by Leonardo da Vinci is considered an archetypal masterpiece, (2) in what year the term masterpiece was first recorded outside a guild context, (3) what is the early variant of masterpiece, (4) which literary work is regarded as a masterpiece of Nigerian literature, and (5) what work apprentices produced to qualify as masters in the guild system.
Summarize the essential aspects of masterpieces.
Mona Lisa is an archetypal masterpiece; the term was recorded in 1605 with Masterprize as an early variant; Things Fall Apart is acclaimed as a masterpiece; and apprentices produced a masterpiece to qualify as masters."
125,353
Aesthetics
Paradigm
https://en.wikipedia.org/wiki/Paradigm
What is the Greek meaning of 'paradigm'?
pattern
From which Greek word is 'paradigm' derived?
παράδειγμα
What does a paradeigma provide in classical rhetoric?
illustrate a similar occurrence
How did Anaximenes define paradeigma?
past actions similar or opposite to current discussion
For what use did scribes apply the term παράδειγμα in Greek texts?
the model for the demiurge's creation of the cosmos
Discuss the concept of paradigm by explaining: (1) its Greek meaning, (2) its derivation, (3) its rhetorical purpose, (4) Anaximenes' definition, and (5) its use by scribes in Greek texts.
Summarize the concept and etymology of paradigm.
Paradigm means 'pattern' and derives from 'παράδειγμα'; it illustrates a similar occurrence in rhetoric, is defined by Anaximenes as past actions similar or opposite to current discussion, and was used by scribes as the model for the demiurge's creation of the cosmos."
99,925
Aesthetics
Literary criticism
https://en.wikipedia.org/wiki/Literary_criticism
What is literary criticism?
study, evaluation, and interpretation of literature
What influences modern literary criticism?
Literary theory
Which two concepts did Aristotle's Poetics develop?
Mimesis and catharsis
Which guide treats literary theory and criticism as identical?
The Johns Hopkins Guide to Literary Theory and Criticism
Why do some critics view literary criticism as practical?
It deals directly with particular literary works
Discuss literary criticism by addressing: (1) what is literary criticism, (2) what influences modern literary criticism, (3) which two concepts did Aristotle's Poetics develop, (4) which guide treats literary theory and criticism as identical, and (5) why do some critics view literary criticism as practical?
Summarize the essentials of literary criticism
Literary criticism is the study, evaluation, and interpretation of literature. It is influenced by literary theory, with Aristotle's Poetics introducing mimesis and catharsis. The Johns Hopkins Guide to Literary Theory and Criticism treats literary theory and criticism as identical, and some critics find literary criticism practical because it deals directly with particular literary works."
92,143
Aesthetics
Escapism
https://en.wikipedia.org/wiki/Escapism
Which Bavarian king was renowned for his escapism related to Richard Wagner's work?
King Ludwig II of Bavaria
In the caricature, what role is this king portrayed in?
King Lohengrin
How does the Oxford English Dictionary define escapism?
Seeking distraction from what must be endured
Which author remarked that jailers are the usual enemies of escape?
C. S. Lewis
Who argued for escapism as creative expression in fantasy literature?
J. R. R. Tolkien
Discuss escapism by addressing: (1) which Bavarian king was renowned for his escapism related to Richard Wagner's work, (2) the role he portrayed in the caricature, (3) how the Oxford English Dictionary defines escapism, (4) which author remarked that jailers are the usual enemies of escape, and (5) who advocated for escapism as creative expression in fantasy literature
Summarize the key aspects of escapism
King Ludwig II of Bavaria embraced escapism as illustrated by his portrayal as King Lohengrin and by seeking distraction from what must be endured; this view is reflected in the insights of C. S. Lewis and J. R. R. Tolkien."
89,373
Aesthetics
Symmetry
https://en.wikipedia.org/wiki/Symmetry
What rotational symmetry does the triskelion exhibit?
3-fold
From which language does the term 'symmetry' originate?
Ancient Greek
What is the opposite of symmetry?
Asymmetry
Into what must a geometric shape be divided to be symmetric?
Two or more identical pieces
How is the fractal-like shape obtained?
Finite subdivision rule
Discuss mathematical symmetry by addressing: (1) what rotational symmetry the triskelion exhibits, (2) from which language the term 'symmetry' originates, (3) what the opposite of symmetry is, (4) what a geometric shape must be divided into to be symmetric, and (5) how a fractal-like shape is obtained
Summarize key aspects of mathematical symmetry
The triskelion exhibits 3-fold symmetry, the term 'symmetry' originates from Ancient Greek, its opposite is asymmetry, a geometric object is symmetric when divided into two or more identical pieces, and a fractal-like shape is obtained through a finite subdivision rule"
81,314
Aesthetics
Golden hour (photography)
https://en.wikipedia.org/wiki/Golden_hour_(photography)
When is the golden hour in photography?
Shortly after sunrise or before sunset
What is another name for the golden hour?
Magic hour
What is the blue hour period?
Before sunrise magic hour and after sunset magic hour. Twighlight.
What is the color temperature during the golden hour?
Approximately 3500 K
What phenomenon in Chicago is known as Chicagohenge?
Sunsets align on east-west streets near equinoxes
Discuss photography lighting by addressing: (1) When is the golden hour in photography? (2) What is another name for the golden hour? (3) What is the blue hour period? (4) What is the color temperature during the golden hour? (5) What phenomenon in Chicago is known as Chicagohenge?
Summarize key aspects of golden hour, blue hour, and Chicagohenge
The golden hour is experienced shortly after sunrise or before sunset and is known as the magic hour; the blue hour occurs before sunrise magic hour and after sunset magic hour; during the golden hour, the light reaches approximately 3500 K; and Chicagohenge marks sunsets aligning on east-west streets near equinoxes"
80,719
Aesthetics
Uncanny
https://en.wikipedia.org/wiki/Uncanny
Where was Repliee Q2 developed?
Osaka University
What phenomenon does Repliee Q2 exemplify?
Uncanny valley
Which essay by Freud elaborated on the uncanny?
Das Unheimliche
Who originally set out the concept of the uncanny?
Ernst Jentsch
Which philosopher raised the question of the uncanny in 1837?
F. W. J. Schelling
Discuss the uncanny by addressing: (1) where Repliee Q2 was developed, (2) which phenomenon it exemplifies, (3) which essay by Freud elaborated on the uncanny, (4) who originally set out the uncanny concept, and (5) which philosopher raised the question in 1837.
Summarize the key aspects of the uncanny.
Repliee Q2 was developed at Osaka University and exemplifies the uncanny valley; Freud's essay Das Unheimliche elaborated on concepts originally set out by Ernst Jentsch, with F. W. J. Schelling raising the uncanny question in 1837."
74,511
Aesthetics
Transcendence (philosophy)
https://en.wikipedia.org/wiki/Transcendence_(philosophy)
What is the literal meaning of 'transcendence' derived from Latin?
Climbing or going beyond
On what are definitions of transcendence generally grounded?
Reason and empirical observation
What does transcendence denote in religious context?
God's nature and power independent of the material universe
What concept contrasts with transcendence in religious thought?
Immanence
Aside from the universe, what else can God transcend?
Knowledge
Discuss transcendence by addressing: (1) its literal Latin meaning, (2) the basis for its definitions, (3) its meaning in religious context, (4) the contrasting concept, and (5) the additional realm God transcends
Summarize the core aspects of transcendence in philosophy and religion
Transcendence literally means climbing or going beyond; it is defined based on reason and empirical observation, and in religious terms, it denotes God's nature and power independent of the material universe, contrasting with immanence, and extending to transcending knowledge"
64,853
Aesthetics
Art for art's sake
https://en.wikipedia.org/wiki/Art_for_art's_sake
What is the usual English rendering of l'art pour l'art?
Art for art's sake
What Greek-derived term means 'complete in itself'?
Autotelic
What Latin phrase is used as a motto by MGM?
ars gratia artis
Who first fully articulated 'art for arts sake' metaphysical meaning?
Théophile Gautier
Who argued in 'The Poetic Principle' for art written solely for its own sake?
Edgar Allan Poe
Discuss art for art's sake by addressing: (1) its usual English rendering, (2) the Greek-derived term meaning 'complete in itself', (3) the Latin phrase used as a motto by MGM, (4) the figure who first articulated its metaphysical meaning, and (5) the author who defended creating art solely for its own sake.
Summarize the concept of art for art's sake.
The phrase "Art for art's sake" encapsulates a self-contained artistic philosophy, described as autotelic, with its Latin version "ars gratia artis" highlighting the idea, first articulated by Théophile Gautier and defended by Edgar Allan Poe."
54,974
Aesthetics
Acquired taste
https://en.wikipedia.org/wiki/Acquired_taste
What is an acquired taste?
Appreciation for things unlikely enjoyed without exposure
What is the opposite of an acquired taste?
Innate taste
What taste do infants prefer at birth?
Sweet
At what age do infants develop salt preference?
Approximately 4-6 months
Which food characteristic, exemplified by sashimi, can hinder enjoyment?
Mouthfeel
Discuss acquired taste by addressing: (1) its definition, (2) its opposite, (3) the taste infants prefer at birth, (4) when they develop salt preference, and (5) which food attribute is illustrated by sashimi.
Provide a brief overview of acquired taste.
Acquired taste is an appreciation for things unlikely enjoyed without exposure and contrasts with innate taste; infants prefer sweet flavors and develop salt preference at approximately 4 months, while mouthfeel is a key food characteristic."
49,539
Aesthetics
Human physical appearance
https://en.wikipedia.org/wiki/Human_physical_appearance
What is human physical appearance defined as?
The outward phenotype or look of humans
Which type of hair remains on adult human body photographs?
Head hair. Terminal Hair.
What is the average weight range for adults?
40 to 80 kg
Compared to chimpanzees, how pronounced is human sexual dimorphism?
More pronounced
Which skin pigmentation predominates in tropical climates?
Darker pigmentation
Discuss human physical appearance by addressing: (1) its definition as the outward phenotype or look of humans, (2) the hair type retained on photographs, (3) the average adult weight range, (4) how human sexual dimorphism compares to that of chimpanzees, and (5) which skin pigmentation dominates in tropical climates.
Summarize key aspects of human physical appearance.
Human physical appearance is the outward phenotype or look of humans, head hair is maintained in photographs, the average adult weight is 40 to 80 kg, sexual dimorphism is more pronounced than in chimpanzees, and darker pigmentation dominates in tropical climates."
37,962
Aesthetics
Postmodernist film
https://en.wikipedia.org/wiki/Postmodernist_film
What does postmodernist film articulate?
themes and ideas of postmodernism
What does postmodernist film test from the audience?
suspension of disbelief
What cultural divide do postmodernist films break down?
between high and low art
When did modernist film mature?
between WWI and WWII
Which theory supports a singular creative vision in film?
auteur theory
Discuss postmodernist film by addressing: (1) what it articulates, (2) what it tests from the audience, (3) what cultural divide it breaks down, (4) when modernist film matured, and (5) which theory supports a singular creative vision in film
Give a brief overview of postmodernist film and modernist cinema
Postmodernist films articulate themes and ideas of postmodernism, test suspension of disbelief, and break down the divide between high and low art, while modernist film matured between WWI and WWII and is associated with the auteur theory."
37,646
Aesthetics
Sexual selection in humans
https://en.wikipedia.org/wiki/Sexual_selection_in_humans
Who introduced the concept of sexual selection?
Charles Darwin
How is sexual selection defined?
Biological mate selection for reproductive success
Which developmental trait is attributed to human sexual selection?
Neoteny
What human anatomical feature evolved due to sexual selection?
Modern human brain
Which model describes sexual selection's development in humans?
Fisherian runaway model
Discuss human evolution by addressing: (1) who introduced sexual selection, (2) how it is defined, (3) which developmental trait it influenced, (4) what anatomical feature evolved due to it, and (5) which model outlines its development
Summarize sexual selection's evolutionary effects on humans
Charles Darwin introduced sexual selection as biological mate selection for reproductive success, linking it to neoteny, the modern human brain, and the Fisherian runaway model."
34,954
Aesthetics
Vulgarity
https://en.wikipedia.org/wiki/Vulgarity
How is vulgarity defined?
Common, coarse, unrefined.
Who claimed that vulgarity can never be self-referential?
John Bayley.
How was 'vulgar' used from the 15th to 17th centuries?
The common language or vernacular.
What new aspect did 'vulgar' acquire from the mid-17th century onward?
It became pejorative.
During which age was vulgarity linked to ostentatious clothing?
Victorian age.
Discuss vulgarity by addressing: (1) how it is defined, (2) who claimed that it can never be self-referential, (3) its use as the common language or vernacular from the 15th to 17th centuries, (4) its shift to a pejorative aspect from the mid-17th century, and (5) its association with the Victorian age.
Summarize the evolution of vulgarity.
Vulgarity is defined as common, coarse, and unrefined. John Bayley claimed that it cannot be self-referential. It originally described the common language or vernacular, later becoming pejorative, and it was notably linked to the Victorian age."
26,872
Aesthetics
Classic
https://en.wikipedia.org/wiki/Classic
In which two parts of speech can 'classic' be used?
Adjective and noun
How is 'classic' used in commerce?
To denote a long-standing popular version
Which ancient cultures are associated with 'The Classics'?
Ancient Greece and Rome
What form of art is more likely called a masterpiece?
Painting, sculpture, literature.
Who first used 'classic' to denote a work of enduring excellence?
Rev. John Bowle
Discuss the term 'classic' by covering: (1) its parts of speech, (2) its commercial usage, (3) its association with ancient Greece and Rome, (4) which art is more likely termed a masterpiece, and (5) its earliest usage by Rev. John Bowle
Provide a brief overview of the term 'classic'
Classic' functions as both an adjective and a noun, is used to denote a long-standing popular version, is linked to Ancient Greece and Rome, contrasts with paintings termed masterpieces, and was first used by Rev. John Bowle"
25,702
Aesthetics
Artistic inspiration
https://en.wikipedia.org/wiki/Artistic_inspiration
What does the Latin word 'inspirare' mean?
to breathe into
What are the cultural origins of inspiration?
Hellenism and Hebraism
In Christianity, inspiration is described as a gift of what?
the Holy Spirit
Which 18th-century philosopher proposed that ideas associate in the mind?
John Locke
Which early 20th-century psychoanalyst located inspiration in the inner psyche?
Sigmund Freud
Discuss inspiration by addressing: (1) What does the Latin word 'inspirare' mean?, (2) What are the cultural origins of inspiration?, (3) In Christianity, inspiration is described as a gift of what?, (4) Which 18th-century philosopher proposed that ideas associate in the mind?, and (5) Which early 20th-century psychoanalyst located inspiration in the inner psyche?
Summarize the diverse cultural and historical aspects of inspiration.
Inspiration means 'to breathe into', is rooted in Hellenism and Hebraism, and in Christianity is viewed as a gift of the Holy Spirit; it is also linked to figures like John Locke and Sigmund Freud"
21,932
Aesthetics
Unattractiveness
https://en.wikipedia.org/wiki/Unattractiveness
How is unattractiveness defined?
Degree to which features are considered aesthetically unfavorable.
Who painted The Ugly Duchess?
Quentin Matsys.
Which philosopher linked his ideas to his struggle with ugliness?
Jean-Paul Sartre.
Which philosopher believed philosophy could redeem outward ugliness?
Socrates.
Which historical figure was noted for his homely appearance?
Abraham Lincoln. Any other is also okay.
Discuss the concept of ugliness by addressing: (1) how unattractiveness is defined, (2) who painted The Ugly Duchess, (3) which philosopher linked his ideas to his struggle with ugliness, (4) which philosopher believed philosophy could redeem outward ugliness, and (5) which historical figure was noted for his homely appearance?
Summarize the key aspects of ugliness including its definition, artistic representation, and philosophical perspective.
Unattractiveness is defined as the degree to which features are considered aesthetically unfavorable; Quentin Matsys represents its artistic side; Jean-Paul Sartre and Socrates offer philosophical insights; and Abraham Lincoln is noted for his homely appearance."
21,202
Aesthetics
Art criticism
https://en.wikipedia.org/wiki/Art_criticism
What is art criticism?
Discussion or evaluation of visual art
What is a goal of art criticism?
To pursue a rational basis for art appreciation
What are the two main divisions of art criticism?
Historical and contemporary (evaluation) criticism
Why are past art critics often ridiculed?
For dismissing now venerated artists
What do artists usually require from critics?
Positive opinions from critics
Discuss art criticism by addressing: (1) what is art criticism, (2) what is its goal, (3) what are its main divisions, (4) why past critics are ridiculed, and (5) what artists require from critics
Summarize key aspects of art criticism
Art criticism is the discussion or evaluation of visual art, it pursues a rational basis for art appreciation, is characterized by historical and contemporary criticism, involves critics ridiculed for dismissing now venerated artists, and requires positive opinions from critics"
20,546
Algebra
Algebra
https://en.wikipedia.org/wiki/Algebra
What does elementary algebra study?
Values solving arithmetic equations
What does abstract algebra study?
Algebraic structures
What does linear algebra investigate?
Linear equations and systems
Which frameworks investigate abstract algebraic patterns?
Universal algebra and category theory
When were algebraic methods first studied?
Ancient period
Discuss algebra by addressing: (1) what does elementary algebra study, (2) what does abstract algebra study, (3) what does linear algebra investigate, (4) which frameworks investigate abstract algebraic patterns, and (5) when were algebraic methods first studied?
Summarize the main branches and foundations of algebra
Elementary algebra focuses on values solving arithmetic equations, abstract algebra examines algebraic structures, and linear algebra investigates linear equations and systems, while universal algebra and category theory provide frameworks for abstract patterns; these methods originated in the ancient period"
364,232
Algebra
Order of operations
https://en.wikipedia.org/wiki/Order_of_operations
What do the rules of order of operations determine?
Which operations to perform first
What is an operation's rank called?
Precedence
Which operation has higher precedence than addition?
Multiplication
When were exponents introduced?
16th and 17th centuries
What can override the standard order of operations?
Parentheses
Discuss the order of operations by addressing: (1) what operations to perform first, (2) what an operation's rank is called, (3) which operation has higher precedence than addition, (4) when exponents were introduced, and (5) what can override the standard order of operations?
Summarize the key principles of the order of operations
The rules determine which operations to perform first, a sequence governed by precedence. Multiplication is executed before addition due to its higher ranking. Exponents were introduced in the 16th and 17th centuries, and parentheses can override these conventions."
312,000
Algebra
Polynomial
https://en.wikipedia.org/wiki/Polynomial
What operations are permitted in a polynomial expression?
Addition, subtraction, multiplication, exponentiation (nonnegative integer powers)
What is an example of a polynomial with a single indeterminate x?
x^2 − 4x + 7
What is an example of a polynomial with three indeterminates?
x^3 + 2xyz^2 − yz + 1
From which two language roots does 'polynomial' derive?
Greek poly and Latin nomen
When was the term 'polynomial' first used?
17th century
Discuss polynomials by addressing: (1) what operations are permitted in a polynomial expression, (2) the example polynomial with a single indeterminate x, (3) the example polynomial with three indeterminates, (4) the language roots of 'polynomial', and (5) when it was first used
Summarize the key aspects of polynomial expressions
Polynomials involve addition, subtraction, multiplication, and exponentiation to nonnegative integer powers; for instance, x^2 − 4x + 7 is a single-indeterminate example while x^3 + 2xyz^2 − yz + 1 illustrates a three-indeterminate case, and the term derives from Greek poly and Latin nomen, first used in the 17th century."
201,749
Algebra
Euler's totient function
https://en.wikipedia.org/wiki/Euler's_totient_function
What does Euler's totient function count?
Positive integers up to n relatively prime to n
What is φ(9) equal to?
6
What is φ(1) equal to?
1
What property does Euler's totient function have for relatively prime numbers?
Multiplicative
Who introduced Euler's totient function?
Leonhard Euler
Discuss Euler's totient function by addressing: (1) what it counts, (2) the value of φ(9), (3) the value of φ(1), (4) its multiplicative property, and (5) who introduced it
Provide a brief overview of Euler's totient function
Euler's totient function counts positive integers up to n relatively prime to n, with φ(9) equal to 6 and φ(1) equal to 1; it is multiplicative and was introduced by Leonhard Euler"
156,225
Algebra
Ratio
https://en.wikipedia.org/wiki/Ratio
What does a ratio represent in mathematics?
It shows how many times one number contains another
What is the literal meaning of ratio?
reason or rational
How many definitions of ratio are in Euclid Elements?
eighteen. 18
How is a ratio represented as a fraction?
First number as numerator, second as denominator
How is a ratio defined in physical sciences?
Dimensionless quotient with same measurement unit
Discuss the concept of ratios by addressing: (1) what a ratio represents in mathematics, (2)literal meaning of ratio, (3) number of definitions of ratio in Euclid elements, (4) how is a ratio represented as a fraction, and (5) how is a ratio defined in physical sciences?
Provide a brief overview of ratios
A ratio shows how many times one number contains another. Ratio literally means reason or rational. In Euclid elements, total number of definitions that relate to ratio are 18. It is represented as a fraction with the first number as numerator and the second as denominator, and in physical sciences, it is defined as a dimensionless quotient with same measurement unit"
115,631
Algebra
History of algebra
https://en.wikipedia.org/wiki/History_of_algebra
What did algebra primarily consist of until the 19th century?
the theory of equations
What type of objects does algebra compute with?
non-numerical mathematical objects
From which Arabic word is 'algebra' derived?
al-jabr
Which medieval Persian mathematician authored the 830 treatise on algebra?
Al-Khwarizmi
What types of equations did al-Khwarizmi’s treatise systematically solve?
linear and quadratic equations
Discuss algebra by addressing: (1) what it primarily consisted of until the 19th century, (2) the type of objects used in its computations, (3) its derivation from an Arabic term, (4) the medieval Persian mathematician who authored its 830 treatise, and (5) the equations solved in that treatise
Summarize the origins and key features of algebra
Algebra originally consisted of the theory of equations and uses non-numerical mathematical objects; its name derives from al-jabr, and Al-Khwarizmi’s treatise systematically solved linear and quadratic equations"
71,115
Algebra
Coefficient
https://en.wikipedia.org/wiki/Coefficient
What is a coefficient in a mathematical expression?
Multiplicative factor in a term
What is a coefficient without units called?
Numerical factor
What is a coefficient with units called?
Constant multiplier
What is the coefficient of the highest degree term called?
Leading coefficient
What is the constant coefficient in the polynomial 2x^2 - x + 3?
3
Discuss the concept of a coefficient by addressing: (1) its definition, (2) the term for a coefficient without units, (3) the term for a coefficient with units, (4) the name for the highest degree term's coefficient, and (5) the constant coefficient in 2x^2 - x + 3
Summarize key coefficient concepts in mathematical expressions
A coefficient is a multiplicative factor in a term. A number without units is a numerical factor, while one with units is a constant multiplier. The highest degree term's coefficient is the leading coefficient, and the constant coefficient in 2x^2 - x + 3 is 3"
70,991
Algebra
Partial fraction decomposition
https://en.wikipedia.org/wiki/Partial_fraction_decomposition
In which year was partial fraction decomposition discovered?
1702
What expressions are the numerator and denominator in a rational fraction?
Polynomials
What degree relationship must each numerator in partial fraction have?
Lower than its irreducible denominator’s degree
What term replaces 'irreducible polynomial' in a coarser decomposition?
Square-free polynomial
In which branch is partial fraction decomposition primarily used?
Algebra
Discuss partial fraction decomposition by addressing: (1) its discovery year, (2) the expressions that constitute a rational fraction, (3) the degree condition of each numerator, (4) the replacement of an irreducible polynomial in a coarser decomposition, and (5) its main field of use
Provide a brief overview of partial fraction decomposition
Discovered in 1702, partial fraction decomposition is an algebraic method applied to rational fractions where both the numerator and denominator are polynomials; each numerator must be of lower degree than its irreducible denominator, and a square-free polynomial is used in place of an irreducible polynomial."
69,971
Algebra
Recurrence relation
https://en.wikipedia.org/wiki/Recurrence_relation
How is the nth term of a sequence defined in a recurrence relation?
A combination of previous terms
What does k represent in a recurrence relation?
Number of previous terms
In a linear recurrence, what is the nth term expressed as?
A linear function of previous k terms
Which famous recurrence relation exemplifies the Fibonacci numbers?
F(n)=F(n-1)+F(n-2)
What are the constant coefficients in the Fibonacci recurrence?
1 and 1
Discuss recurrence relations by addressing: (1) how the nth term is defined, (2) what k represents, (3) what a linear recurrence expresses the nth term as, (4) the famous Fibonacci recurrence, and (5) its constant coefficients
Summarize the concept of recurrence relations
Recurrence relations define the nth term as a combination of previous terms with k indicating the number of terms used; in linear recurrences, the nth term is given by a linear function, as seen in the Fibonacci recurrence F(n)=F(n-1)+F(n-2) which employs constant coefficients of 1 and 1"
66,234
Algebra
Closed-form expression
https://en.wikipedia.org/wiki/Closed-form_expression
Which arithmetic operations are permitted in closed-form expressions?
Addition, subtraction, multiplication, division, and integer powers
What functions are commonly allowed in closed-form expressions?
n-th root, exponential function, logarithm, and trigonometric functions
Which formula is a closed-form solution for quadratic equations?
Quadratic formula
What does the Abel–Ruffini theorem imply about higher degree equations?
They cannot be expressed in radicals
For which polynomial equations are radical expressions available for all solutions?
Cubic and quartic equations
Discuss closed-form expressions by addressing: (1) which arithmetic operations are permitted, (2) which functions are commonly allowed, (3) the closed-form solution for quadratic equations, (4) the implication of the Abel–Ruffini theorem, and (5) the polynomial equations with complete radical expressions
Provide a brief overview of closed-form expressions in mathematics
Closed-form expressions use addition, subtraction, multiplication, division, and integer powers, and employ n-th root, exponential function, logarithm, and trigonometric functions; the quadratic formula exemplifies a closed-form solution, yet some higher degree equations cannot be expressed in radicals while cubic and quartic equations do have radical solutions"
60,270
Algebra
Square (algebra)
https://en.wikipedia.org/wiki/Square_(algebra)
What operation does 'square' denote in mathematics?
Multiplying a number by itself
What is the square of 3?
9
What adjective corresponds to squaring?
Quadratic
What is (x+1) squared equal to?
x^2 + 2x + 1
What identity shows the square function is even?
x^2 = (-x)^2
Discuss the squaring operation by addressing: (1) what operation 'square' denotes, (2) what the square of 3 is, (3) which adjective corresponds to squaring, (4) what (x+1) squared equals, and (5) what identity shows the square function is even.
Summarize the key aspects of squaring in mathematics.
Squaring involves multiplying a number by itself, with 3 squared equal to 9. It is described as quadratic, yields x^2 + 2x + 1 when applied to (x+1), and satisfies the identity x^2 = (-x)^2"
51,893
Algebra
Operator (mathematics)
https://en.wikipedia.org/wiki/Operator_(mathematics)
What is an operator in mathematics?
A mapping acting on elements of a space
What is the most common mathematical operator?
Linear operator
What are the most basic mathematical operators?
Linear maps on vector spaces
What else does the term 'operator' denote in mathematics?
The symbol of a mathematical operation
What equality defines a linear mapping A:U→V?
A(αx+βy)=αAx+βAy
Discuss operators by addressing: (1) What is an operator in mathematics?, (2) How is an operator's domain often described?, (3) What are the most basic operators?, (4) What else does the term 'operator' denote in mathematics?, (5) What equality defines a linear mapping A:U→V?
Summarize the concept of operators in mathematics
An operator is a mapping acting on elements of a space whose domain is difficult to characterize explicitly; the simplest operators are linear maps on vector spaces, the term also denotes the symbol of a mathematical operation, and a linear mapping satisfies A(αx+βy)=αAx+βAy"
51,616
Algebra
Cyclotomic polynomial
https://en.wikipedia.org/wiki/Cyclotomic_polynomial
What type of polynomial is the nth cyclotomic polynomial?
Unique irreducible polynomial with integer coefficients
Which polynomial does the nth cyclotomic polynomial divide?
x^n - 1
What are the roots of the nth cyclotomic polynomial?
nth primitive roots of unity
How is Φ_n(x) expressed for a prime n?
1+x+x^2+...+x^(n-1)
What product relation links cyclotomic polynomials to x^n - 1?
∏_{d|n}Φ_d(x)=x^n−1
Discuss the cyclotomic polynomial by addressing: (1) its unique irreducible nature, (2) its role as a divisor of x^n - 1, (3) its roots as nth primitive roots of unity, (4) its expression as 1+x+x^2+...+x^(n-1) for a prime n, and (5) the relation ∏_{d|n}Φ_d(x)=x^n−1
Provide a brief overview of cyclotomic polynomials
The cyclotomic polynomial is a unique irreducible polynomial with integer coefficients; it divides x^n - 1, its roots are the nth primitive roots of unity, it is expressed as 1+x+x^2+...+x^(n-1) for a prime n, and the product relation ∏_{d|n}Φ_d(x)=x^n−1 holds."
46,646
Algebra
Canonical form
https://en.wikipedia.org/wiki/Canonical_form
What conclusion is drawn when sorted strings agree?
They are anagrams.
What is a canonical form?
A standard representation of an object.
What is the canonical form of a positive integer?
A finite digit sequence without a leading zero.
Why is canonical form used in computer algebra?
It ensures a unique representation.
How is the equality of objects tested?
By comparing their canonical forms.
Discuss the concepts by addressing: (1) what conclusion is drawn when sorted strings agree, (2) what is a canonical form, (3) what is the canonical form of a positive integer, (4) why is canonical form used in computer algebra, and (5) how is the equality of objects tested.
Give a brief overview of canonical forms and anagram testing.
When sorted strings agree, they are anagrams. A canonical form is a standard representation of an object, exemplified by a finite digit sequence without a leading zero for positive integers. It ensures a unique representation, allowing object equality to be tested by comparing canonical forms."
41,942
Algebra
Elementary algebra
https://en.wikipedia.org/wiki/Elementary_algebra
What is the quadratic formula?
x = -b ± √(b²-4ac)/(2a)
Which equation does the quadratic formula solve?
ax² + bx + c = 0
What must be true about coefficient a in qudratic equation?
a ≠ 0
What do the symbols a, b, and c represent in quadratic equation?
Arbitrary numbers
What unique element does algebra introduce compared to arithmetic?
Variables
Discuss basic algebra by addressing: (1) what is the quadratic formula, (2) which equation does it solve, (3) what must be true about coefficient a, (4) what do the symbols a, b, and c represent, and (5) what unique element does algebra introduce compared to arithmetic?
Give a brief overview of elementary algebra.
x = -b ± √(b²-4ac)/(2a) is the quadratic formula that solves ax² + bx + c = 0, where a ≠ 0, with a, b, and c as arbitrary numbers, and algebra introduces variables."
41,622
Algebra
Kernel (algebra)
https://en.wikipedia.org/wiki/Kernel_(algebra)
What element's inverse image defines a homomorphism's kernel in additive notation?
0
What is another name for the kernel of a matrix?
null space
When is a homomorphism's kernel reduced to just 0 (or 1)?
when injective
According to the fundamental theorem on homomorphisms, what is the image isomorphic to?
the quotient by the kernel
When a single-element inverse image is insufficient, what does the kernel become?
a congruence relation
Discuss the kernel of a homomorphism by addressing: (1) the defining element in additive notation, (2) an alternate name for the kernel of a matrix, (3) the condition under which the kernel is 0 (or 1), (4) the isomorphism stated by the fundamental theorem on homomorphisms, and (5) what the kernel becomes when a single-element inverse image does not determine injectivity.
Summarize the critical aspects of kernels in algebra.
A homomorphism’s kernel is defined as the inverse image of 0; as a matrix's kernel it is known as the null space; it is reduced to 0 when injective; the fundamental theorem shows its image is isomorphic to the quotient by the kernel; and when a single-element inverse image is insufficient, it becomes a congruence relation."
34,452
Algebra
Irreducible polynomial
https://en.wikipedia.org/wiki/Irreducible_polynomial
What is an irreducible polynomial?
It cannot be factored into two non-constant polynomials
On what does a polynomial's irreducibility depend?
Its coefficient ring
How does x² − 2 factor over the reals?
(x−√2)(x+√2)
Over which ring is x² − 2 irreducible?
Integers
What is a polynomial that is not irreducable called?
Reducable polynomial
Discuss irreducible polynomials by addressing: (1) what is an irreducible polynomial, (2) on what its irreducibility depends, (3) how x² − 2 factors over the reals, (4) over which ring x² − 2 is irreducible, and (5) opposite of irreducable polynomials?
Summarize the concept of polynomial irreducibility
An irreducible polynomial cannot be factored into two non-constant polynomials and depends on its coefficient ring; for instance, x² − 2 factors as (x−√2)(x+√2) over the reals while remaining irreducible over the integers, and polynomial which is not irreducable is called a reducable polynomial.
30,005
Algebra
Digital root
https://en.wikipedia.org/wiki/Digital_root
What is the digital root of 12345 in base 10?
6
What iterative process computes the digital root?
Iterative summing of digits
In base 10, the digital root is equivalent to taking the remainder upon division by which number?
9
What expression gives the number of digits in base b?
⌊log_b n⌋+1
When is a natural number considered a digital root?
When F_b(n)=n
Discuss the digital root concept by addressing: (1) What is the digital root of 12345 in base 10?, (2) What iterative process computes the digital root?, (3) In base 10, the digital root is equivalent to taking the remainder upon division by which number?, (4) What expression gives the number of digits in base b?, (5) When is a natural number considered a digital root?
Provide a brief overview of digital roots.
The digital root of 12345 in base 10 is 6, obtained by iterative summing of digits, with a base-10 shortcut using division by 9, while the number of digits in base b is given by ⌊log_b n⌋+1 and a number is considered a digital root when F_b(n)=n"
28,258
Algebra
Operand
https://en.wikipedia.org/wiki/Operand
What is an operand in mathematics?
Quantity operated on by a mathematical operation
What is the first operand in '3 + 6 = 9'?
3
What is the second operand in '3 + 6 = 9'?
6
In '(3 + 5) × 2', which operand is nested?
(3 + 5)
What notation is most common in everyday usage?
Infix notation
Discuss operands by addressing: (1) their definition in mathematics, (2) the first operand in '3 + 6 = 9', (3) the second operand in '3 + 6 = 9', (4) the nested operand in '(3 + 5) × 2', and (5) the common notation used
Summarize operands and their usage in arithmetic operations
An operand is a quantity operated on by a mathematical operation; in '3 + 6 = 9' the operands are 3 and 6, and in '(3 + 5) × 2' the nested operand is (3 + 5), with infix notation being most common"
28,070
Algebra
Monomial
https://en.wikipedia.org/wiki/Monomial
How many terms does a monomial have?
One term
What type of exponents are used on variables in a monomial’s power product?
Nonnegative integers
Which constant is considered a primitive monomial?
1
For a single variable, what forms can a monomial take?
1 or x^n (n positive)
In Laurent series, what type of exponents may appear in a monomial?
Negative
Discuss monomials by addressing: (1) how many terms they contain, (2) the type of exponents in their power product form, (3) the primitive monomial constant, (4) their form when involving a single variable, and (5) the exponent type in Laurent series
Summarize the key properties of a monomial
A monomial has one term with nonnegative integer exponents; its primitive form is 1; in a single variable, it is 1 or x^n (n positive); and in Laurent series, exponents may be negative"
27,300
Algebra
Inverse element
https://en.wikipedia.org/wiki/Inverse_element
In an operation ∗, if x ∗ y equals the identity element, what is x called?
Left inverse of y
In an operation ∗, if x ∗ y equals the identity element, what is y called?
Right inverse of x
Under what condition are left and right inverses equal and unique?
When ∗ is associative
What is an invertible element in a ring called?
Unit
How is the multiplicative inverse of a fraction determined?
By exchanging numerator and denominator
Discuss the generalization of inverse elements by addressing: (1) what is x called when x ∗ y equals the identity element, (2) what is y called in that circumstance, (3) under what condition left and right inverses are equal and unique, (4) what is an invertible element in a ring called, and (5) how is the multiplicative inverse of a fraction determined?
Summarize the concept and properties of inverse elements
An element x is the left inverse of y when x ∗ y equals the identity element and y is the right inverse of x; when ∗ is associative, these inverses are equal and unique, and in a ring, an invertible element is called a unit, with the multiplicative inverse of a fraction obtained by exchanging its numerator and denominator"
25,086
Algebra
Module homomorphism
https://en.wikipedia.org/wiki/Module_homomorphism
What equality defines the additive preservation in a module homomorphism?
f(x+y)=f(x)+f(y)
In left modules, how is scalar multiplication preserved?
f(rx)=rf(x)
How is the kernel of a module homomorphism defined?
Preimage of zero element
What is the notation for the set of all module homomorphisms from M to N?
Hom_R(M,N)
What condition makes a module homomorphism an isomorphism?
It admits an inverse homomorphism
Discuss module homomorphisms by addressing: (1) how addition is preserved (f(x+y)=f(x)+f(y)), (2) how scalar multiplication is preserved (f(rx)=rf(x)), (3) what the kernel is, (4) the notation for the homomorphism set, and (5) when a homomorphism is an isomorphism.
Summarize the core properties of module homomorphisms over a ring.
A module homomorphism satisfies f(x+y)=f(x)+f(y) and f(rx)=rf(x), its kernel is the preimage of the zero element, and the set of these maps is denoted by Hom_R(M,N); it is an isomorphism if it admits an inverse homomorphism."
22,932
Algebra
Constant (mathematics)
https://en.wikipedia.org/wiki/Constant_(mathematics)
What does 'constant' mean as an adjective in mathematics?
Non-variance
What does a constant function do?
Always returns the same value
How is a general quadratic function expressed?
ax²+bx+c
What does the constant term in a polynomial represent?
Coefficient of x^0
Which constant function example is given for a single variable?
f(x)=5
Discuss the concept of constant by addressing: (1) what 'constant' means as an adjective in mathematics, (2) what a constant function does, (3) how a general quadratic function is expressed, (4) what the constant term in a polynomial represents, and (5) which constant function example is given for a single variable.
Provide a brief overview of mathematical constants and constant functions.
In mathematics, 'constant' means non-variance; a constant function always returns the same value, as seen in f(x)=5; a general quadratic function is expressed as ax²+bx+c, where the constant term is the coefficient of x^0"
22,848
Algebra
Consistent and inconsistent equations
https://en.wikipedia.org/wiki/Consistent_and_inconsistent_equations
What is a system of equations called if it has at least one solution?
consistent
What is a system of equations called if it has no solution?
inconsistent
What false equation exemplifies a contradiction?
2 = 1
When is a linear system consistent?
When its coefficient matrix has the same rank as agumented matrix
In the system x+y+z=3, x+y+2z=4, what is the coefficient of of x in equation 1?
1
Discuss systems of equations by addressing: (1) what they are called if a solution exists, (2) what they are called if no solution exists, (3) which false equation exemplifies contradiction, (4) when is a linear system consistent, and (5) In the system x+y+z=3, x+y+2z=4, what is the coefficient of of x in equation 1?
Summarize the key concepts of consistent and inconsistent systems of equations
A system is consistent when it has at least one solution and inconsistent when it has none; the false equation 2 = 1 illustrates a contradiction. A linear system is consistent when its coefficient matrix has the same rank as augmented matrix. Lastly, cofficient of x in equation 1 is 1.
19,298
Algebra
Series expansion
https://en.wikipedia.org/wiki/Series_expansion
What is a series expansion?
Infinite sum of simpler functions
What is a Taylor series?
Power series based on derivatives
What is a Maclaurin series?
Taylor series at zero
What is a Laurent series?
Generalized series allowing negative exponents
What notation describes approximation error?
Big O notation
Discuss series expansions by addressing: (1) what is a series expansion, (2) what is a Taylor series, (3) what is a Maclaurin series, (4) what is a Laurent series, and (5) what notation describes approximation error.
Summarize series expansion techniques.
A series expansion is an infinite sum of simpler functions; a Taylor series is a power series based on derivatives with its Maclaurin series at zero; a Laurent series is a generalized series allowing negative exponents; and Big O notation describes the approximation error."
16,578
Algebra
Permanent (mathematics)
https://en.wikipedia.org/wiki/Permanent_(mathematics)
How is the permanent of an n×n matrix defined?
Sum over all permutations of the product of entries
Which group's elements are summed over in the permanent's definition?
The symmetric group S_n
What key difference distinguishes the permanent from the determinant?
Permutation signatures are not considered
Which notation does Minc use for the permanent of rectangular matrices?
Per(A)
Who originated the term 'permanent' in 1812?
Cauchy
Discuss the permanent by addressing: (1) its definition as a sum over all permutations of the product of entries, (2) the group over which the summation is performed, (3) its difference from the determinant regarding permutation signatures, (4) Minc's notation for rectangular matrices, and (5) the origin of its name in 1812
Summarize the key aspects of the matrix permanent
The permanent of a matrix is computed as the sum over all permutations of the product of its entries, taken over the symmetric group S_n; it ignores permutation signatures, Minc denotes it as Per(A) for rectangular matrices, and it was originally coined by Cauchy in 1812."
14,540
Algebra
Factorization of polynomials over finite fields
https://en.wikipedia.org/wiki/Factorization_of_polynomials_over_finite_fields
What does polynomial factorization decompose a polynomial into?
Product of irreducible factors
Is polynomial factorization unique for coefficients in any field?
Yes, unique
What alternative name is given for a finite field?
Galois field
What can be the order of a finite field?
Prime or prime power
What is a polynomial with more than one indeterminate called?
multivariate polynomials
Discuss polynomial factorization by addressing: (1) what it decomposes a polynomial into, (2) whether it is unique for field coefficients, (3) the alternative name for a finite field, (4) what form the order of a finite field takes, and (5) which type of polynomials have more than one indeterminate?
Summarize polynomial factorization and finite fields
Polynomial factorization decomposes a polynomial into a product of irreducible factors and is unique; a finite field, also known as a Galois field, has an order that is a prime or prime power, and multivariate polynomials have more than one indeterminate"
12,770
Algebra
Nested radical
https://en.wikipedia.org/wiki/Nested_radical
What is a nested radical in algebra?
A radical expression containing another radical expression.
Which nested radical appears in the discussion of the regular pentagon?
√(5-2√5)
What does denesting refer to in algebra?
Rewriting a nested radical in non-nested form.
What restriction is placed on c in the two nested square roots theorem?
c is not a square of a rational number.
What is the denested form of √(3+2√2)?
1+√2
Discuss nested radicals by addressing: (1) what is a nested radical in algebra, (2) which nested radical appears in the discussion of the regular pentagon, (3) what denesting refers to, (4) what restriction is placed on c in the two nested square roots theorem, and (5) what is the denested form of √(3+2√2)?
Give a brief overview of nested radicals and denesting.
A nested radical is a radical expression containing another radical expression; for example, √(5-2√5) appears in the context of a regular pentagon. Denesting is the process of rewriting such an expression in non-nested form, and the associated theorem requires that c is not a square of a rational number. An instance of denesting is demonstrated when √(3+2√2) is rewritten as 1+√2."
11,709
Anthropology
Anthropology
https://en.wikipedia.org/wiki/Anthropology
What is anthropology defined as?
The scientific study of humanity
What does social anthropology study?
Patterns of behavior
What does linguistic anthropology examine?
Language's influence on social life
What does biological anthropology study?
Biological development of humans
Who is considered the founder of modern anthropology?
Bernardino de Sahagún
Discuss anthropology by addressing: (1) its definition, (2) what social anthropology studies, (3) what linguistic anthropology examines, (4) what biological anthropology studies, and (5) who is considered the founder of modern anthropology
Provide a brief summary of anthropology
Anthropology is the scientific study of humanity, with social anthropology focusing on patterns of behavior, linguistic anthropology examining language's influence on social life, and biological anthropology studying the biological development of humans; Bernardino de Sahagún is considered the founder of modern anthropology"
6,575,462
Anthropology
Shrunken head
https://en.wikipedia.org/wiki/Shrunken_head
Which culture exclusively practiced ritualistic head shrinking?
Jivaroan
What do Shuar people call a shrunken head?
Tsantsa
Which part of the head exhibits shrinkage?
Lateral sides of the forehead
What is the initial step in creating a shrunken head?
Removing the skull from the neck
What object is used to maintain the head's form in shrunken head?
A wooden ball
Discuss shrunken heads by addressing: (1) which culture exclusively practiced ritualistic head shrinking, (2) what Shuar people call a shrunken head, (3) which part of the head exhibits shrinkage, (4) the initial step in creating a shrunken head, and (5) the object used to maintain its form.
Give a brief overview of shrunken head preparation.
The Shuar exclusively practiced head shrinking and called their shrunken heads tsantsa; their process began by removing the skull from the neck, which produced shrinkage on the lateral sides of the forehead and involved using a wooden ball to maintain the head’s form."
167,361
Anthropology
Social class
https://en.wikipedia.org/wiki/Social_class
What are the three most common social classes?
Working, middle, upper class
What term is social class synonymous with in everyday language?
Socioeconomic class
Who defined class by one's relationship to the means of production?
Karl Marx
According to Karl Marx, what is distinct about the bourgeoisie?
They do not work
According to academics, what does social class refer to?
Stable cultural background
Discuss hierarchical stratification by addressing: (1) what are the three most common social classes, (2) what term is social class synonymous with in everyday language, (3) who defined class by one's relationship to the means of production, (4) according to Karl Marx, what is distinct about the bourgeoisie, and (5) according to academics, what does social class refer to?
Summarize social class and hierarchical stratification in societies.
The most common social classes are the working, middle, and upper class, also known as socioeconomic class. Karl Marx defined class by its relation to the means of production, noting that the bourgeoisie do not work, while academics view social class as a stable cultural background."
163,959
Anthropology
Kinship
https://en.wikipedia.org/wiki/Kinship
What is kinship in anthropology?
The web of social relationships
What does study of kinship entail?
It entails the study of what humans do with basic facts of life like mating, gestation, parenthood, socialization.
What are kinship relations through marriage called?
Affinity
What social process does kinship facilitate?
Socialization of children
What term describes kin relationships from one's group of origin?
Descent group
Discuss kinship by addressing: (1) its definition in anthropology, (2) what study of kinship entail, (3) the term for marriage-based kinship, (4) the social process it facilitates, and (5) the term for kin relationships from one's group of origin
Summarize the concept of kinship in human societies
Kinship is the web of social relationships. Robin Fox highlights its role, with marriage-based connections called affinity and group-origin ties known as descent group, all of which facilitate the socialization of children."
98,416
Anthropology
Human geography
https://en.wikipedia.org/wiki/Human_geography
In which year was the Royal Geographical Society founded?
1830
When was the first professor of geography in the UK appointed?
1883
Who was the first major geographical intellect in the UK?
Halford John Mackinder
Which society was founded in the United States in 1888?
National Geographic Society
Which map depicted the 1854 Broad Street cholera outbreak?
John Snow's 1854 cholera map
Discuss human geography history by addressing: (1) the founding year of the Royal Geographical Society, (2) the appointment year of the first UK geography professor, (3) the identity of the first major geographical intellect in the UK, (4) the society founded in the United States in 1888, and (5) the map of the 1854 Broad Street cholera outbreak.
Summarize key historical milestones in human geography.
Founded in 1830, the Royal Geographical Society marked an academic milestone; in 1883, the first UK geography professor was appointed, leading to Halford John Mackinder emerging as a key intellectual, followed by the establishment of the National Geographic Society and exemplified by John Snow's 1854 cholera map."
76,703
Anthropology
Cultural identity
https://en.wikipedia.org/wiki/Cultural_identity
What is cultural identity defined as?
A feeling of belonging to a group.
How can cultural identity be expressed?
Through styles of clothing or aesthetic markers, arts.
What are the three components of a person's cultural identity?
Cultural knowledge, category label, and social connections.
What is the first step in developing cultural identity?
Immersion in cultural values, beliefs, and practices.
What determines a clear cultural identity?
Fewer cultural identity changes.
Discuss cultural identity by addressing: (1) What is cultural identity defined as?, (2) How can cultural identity be expressed?, (3) What are the three components of a person's cultural identity?, (4) What is the first step in developing cultural identity?, (5) What determines a clear cultural identity?
Summarize the key aspects of cultural identity.
Cultural identity is a feeling of belonging to a group expressed through styles of clothing or aesthetic markers, comprises cultural knowledge, category label, and social connections, develops through immersion in cultural values, beliefs, and practices, and is clearer when there are fewer cultural identity changes."
76,001
Anthropology
Endocannibalism
https://en.wikipedia.org/wiki/Endocannibalism
What is endocannibalism?
Eating human remains from one's community
Which ancient historian mentioned funerary cannibalism among the Callatiae?
Herodotus
Which indigenous group in western Brazil practiced endocannibalism as an act of compassion?
Wari' people
What did the Amahuaca Indians of Peru do with cremated bone particles?
Ground them with corn to form gruel
What was the first infectious human prion disease discovered?
Kuru
Explain endocannibalism by addressing: (1) its definition, (2) the ancient historian who mentioned funerary cannibalism among the Callatiae, (3) the indigenous group in western Brazil that practiced it compassionately, (4) the method used by the Amahuaca Indians of Peru with cremated bone particles, and (5) the first discovered infectious human prion disease.
Provide a brief overview of endocannibalism and its medical implications
Endocannibalism is the practice of eating human remains from one's community. Herodotus documented funerary cannibalism among the Callatiae. The Wari' people practiced it compassionately, while the Amahuaca Indians ground cremated bone particles with corn to form gruel. Kuru was the first identified infectious human prion disease."
52,041
Anthropology
Basic needs
https://en.wikipedia.org/wiki/Basic_needs
What does the basic needs approach define?
Absolute minimum resources for long-term physical well-being
How is the poverty line defined?
Income required to satisfy people's needs
Which conference introduced the basic needs approach?
International Labour Organization's World Employment Conference
What items are included in the traditional basic needs list?
Food, shelter, and clothing
What concept did Amartya Sen emphasize?
Capabilities
Explain the basic needs approach by addressing: (1) what it defines, (2) how the poverty line is defined, (3) which conference introduced it, (4) what comprises the traditional basic needs list, and (5) what concept Amartya Sen emphasized
Summarize the basic needs approach to poverty measurement
The approach defines the absolute minimum resources needed for long-term well-being, sets the poverty line as the income required to satisfy people's needs, was introduced by the International Labour Organization's World Employment Conference, traditionally includes food, shelter, and clothing, and emphasizes capabilities as highlighted by Amartya Sen."
49,179
Anthropology
Culture shock
https://en.wikipedia.org/wiki/Culture_shock
Which group confused Europeans with prophets from the east?
Aztecs
How many distinct phases of culture shock are described?
Four
What is the first phase of culture shock?
honeymoon
What common problem related to culture shock involves excessive information?
information overload
Can culture shock be completely prevented?
No
Discuss culture shock by addressing: (1) which group confused Europeans with prophets from the east, (2) how many distinct phases of culture shock are described, (3) what is the first phase of culture shock, (4) what common problem related to culture shock involves excessive information, and (5) whether culture shock can be completely prevented.
Summarize key points about culture shock.
The Aztecs experienced culture shock, which consists of four phases starting with the honeymoon phase; a common challenge is information overload, and it cannot be completely prevented."
48,169
Anthropology
Nations and IQ
https://en.wikipedia.org/wiki/Nations_and_IQ
When did the debate on national IQ differences start?
Early 2000's
Who constructed and published early IQ estimates?
Richard Lynn and Tatu Vanhanen
Which organization described Lynn's datasets as unscientific in 2020?
European Human Behavior and Evolution Association
In what year was the European IQ article published?
1981
In which year did Lynn and Vanhanen publish their IQ books?
2002
Discuss the national IQ debate by addressing: (1) when it began, (2) who constructed early IQ estimates, (3) which organization labeled Lynn's datasets unscientific in 2020, (4) the publication year of the European IQ article, and (5) the year of Lynn and Vanhanen’s IQ books
Summarize the controversy in national IQ studies
The debate began in the early 2000's when Richard Lynn and Tatu Vanhanen published early IQ estimates; the European Human Behavior and Evolution Association described Lynn's datasets as unscientific in 2020; an international IQ article was published in 1981; and their IQ books were released in 2002."
41,502
Anthropology
Progress
https://en.wikipedia.org/wiki/Progress
What is progress defined as?
Movement towards a perceived refined, improved, or desired state
Which philosophy regards progress as central?
Progressivism
During which century was progress introduced in social theories?
Early-19th century
Which economic indicator is criticized as a flawed measure of progress?
GDP growth
Which website is set up to share information on evaluating societal progress?
Wikiprogress
Discuss progress by addressing: (1) what progress is defined as, (2) which philosophy holds it as central, (3) during which century it was introduced in social theories, (4) which economic indicator is criticized, and (5) which website shares information on evaluating societal progress
Summarize the concept and measurement of progress
Progress is movement towards a perceived refined, improved, or desired state, a core idea in progressivism that emerged in early-19th century social theories; GDP growth is used as an economic measure, and Wikiprogress shares information on evaluating progress."
38,101
Anthropology
Poppet
https://en.wikipedia.org/wiki/Poppet
What is a poppet in folk magic?
A doll representing a person.
Where are poppets occasionally found?
Lodged in chimneys.
What is the etymological origin of 'poppet'?
Older Middle English spelling of 'puppet'.
What role do poppets serve in folk magic?
They serve as spirit bridges.
Where did the first written mentions of the kitchen witch poppet originate?
England.
Discuss poppets in folk magic by addressing: (1) what a poppet is, (2) where poppets are occasionally found, (3) the etymological origin of 'poppet', (4) the role of poppets as spirit bridges, and (5) where the first written mentions of the kitchen witch poppet originated.
Provide a brief overview of poppets in folk magic and witchcraft.
Poppets are dolls representing a person that are occasionally lodged in chimneys; their name is derived from an older Middle English spelling of 'puppet' and they serve as spirit bridges in folk magic, with the earliest written mentions of the kitchen witch poppet originating in England."
35,494
Anthropology
Ceremony
https://en.wikipedia.org/wiki/Ceremony
How is a ceremony defined?
A unified ritualistic event with a purpose
What is the etymological origin of the word 'ceremony'?
Etruscan via Latin caerimonia
How do religious and civil ceremonies compare in Western countries?
They share similar values and ideals
What term did Dally Messenger use to describe the difference between ceremonies?
Supernatural infrastructure
Which food item in marriage ceremonies originates from pre-Christian Roman traditions?
Wedding cake
Discuss ceremony by addressing: (1) its definition, (2) its etymological origin, (3) the similarity of religious and civil ceremonies, (4) the term used for their difference, and (5) the traditional food item in marriage ceremonies
Summarize the key elements of ceremonial events
A ceremony is a unified ritualistic event with a purpose. Its term comes from Etruscan via Latin caerimonia, and such events share similar values and ideals. They differ in supernatural infrastructure, and a wedding cake is a traditional element in marriage ceremonies."
32,285
Anthropology
Cultural diffusion
https://en.wikipedia.org/wiki/Cultural_diffusion
Who conceptualized cultural diffusion?
Leo Frobenius
What is the title of the publication that introduced cultural diffusion?
Der westafrikanische Kulturkreis
Which type diffusion involves an innovation remaining strong in its source area while spreading outward?
Expansion diffusion
Which type diffusion describes an idea migrating into new areas while leaving its origin behind?
Relocation diffusion
Which type diffusion spreads from larger to smaller places, often under elite influence?
Hierarchical diffusion
Discuss cultural diffusion by addressing: (1) who conceptualized it, (2) the title of the publication that introduced it, (3) which diffusion type involves an innovation remaining strong in its source area while spreading outward, (4) which diffusion type describes an idea migrating into new areas while leaving its origin behind, and (5) which diffusion type spreads from larger to smaller places, often under elite influence?
Provide a brief overview of cultural diffusion
Leo Frobenius introduced cultural diffusion in Der westafrikanische Kulturkreis, highlighting Expansion diffusion, Relocation diffusion, and Hierarchical diffusion as key types."
30,158
Anthropology
Non-place
https://en.wikipedia.org/wiki/Non-place
Who coined the term non-place?
Marc Augé
What is the title of the work introducing non-place?
Non-places: introduction to an anthropology of supermodernity
Which scholar's earlier concept does non-place resemble?
Edward Relph
What does an anthropological place offer people?
Empowers identity
What is a key characteristic of non-place?
Anonymous and lonely
Discuss the concept of non-place by addressing: (1) who coined the term non-place, (2) the title of the work where it was introduced, (3) which scholar's concept it resembles, (4) what an anthropological place offers people, and (5) what characterizes a non-place.
Summarize the concept of non-place.
Marc Augé coined non-place in his work titled Non-places: introduction to an anthropology of supermodernity; it resembles Edward Relph's concept, and while anthropological places empower identity, non-places are anonymous and lonely."
29,678
Anthropology
Doxa
https://en.wikipedia.org/wiki/Doxa
What does the Greek term doxa mean?
Common belief or popular opinion
In classical rhetoric, what is doxa contrasted with?
Episteme
From which Greek verb is doxa derived?
Dokein
During which centuries did doxa acquire a meaning of 'glory'?
Between 3rd and 1st centuries BC
Which philosopher described doxa as an irrational belief in the lower parts of the soul?
Plato
Discuss doxa by addressing its definition as common belief or popular opinion, its contrast with episteme, its derivation from dokein, the period it gained a 'glory' meaning, and the philosopher who critiqued it.
Summarize the concept and origin of doxa.
Doxa signifies common belief or popular opinion and is contrasted with episteme; it is derived from dokein, acquired a 'glory' meaning between the 3rd and 1st centuries BC, and was critiqued by Plato as an irrational belief."
28,750
Anthropology
Kinship terminology
https://en.wikipedia.org/wiki/Kinship_terminology
What is kinship terminology?
A system for referring to an individual's relatives.
Which two types of uncles do some languages distinguish?
Consanguine and affinal uncles.
What two distinctions do most kinship terminologies make?
Sex and generation.
What two relationship types do kinship terminologies differentiate?
Blood and marriage.
Who performed the first survey of kinship terminologies?
Lewis Henry Morgan.
Discuss kinship terminology by addressing: (1) what it is, (2) which two types of uncles are distinguished, (3) what two distinctions are made, (4) which relationship types are differentiated, and (5) who performed the first kinship survey.
Provide a brief overview of kinship terminology.
Kinship terminology is a system for referring to an individual's relatives, distinguishing consanguine and affinal uncles, making distinctions based on sex and generation, differentiating blood and marriage relationships, and was first surveyed by Lewis Henry Morgan."
27,413
Anthropology
Chinese kinship
https://en.wikipedia.org/wiki/Chinese_kinship
How is the Chinese kinship system's complexity described?
Among the world's most complicated
Through which familial line is descent traced in traditional Chinese kinship?
Male line
What residence practice characterizes traditional Chinese kinship?
Patrilocal residence
When do children join the kinship system in China?
From birth
Whose will prevails in family conflicts in chinese kinship?
Superior family member
Discuss the Chinese kinship system by addressing: (1) how its complexity is described, (2) the familial line used for descent, (3) the characteristic residence practice, (4) when children join the system, and (5) whose will prevails in conflicts
Summarize key aspects of the Chinese kinship system
The Chinese kinship system is among the world's most complicated, relying on a male line and patrilocal residence, with children joining from birth and conflicts resolved by the superior family member."
25,560
Anthropology
Thick description
https://en.wikipedia.org/wiki/Thick_description
Who first introduced the concept of thick description?
Gilbert Ryle
In which year was thick description introduced by Gilbert Ryle?
1968
Who developed the predominant modern sense of thick description?
Clifford Geertz
What is the title of Clifford Geertz's influential ethnographic book?
The Interpretation of Cultures
Which literary criticism movement employs thick description?
New Historicism
Discuss thick description by addressing: (1) who first introduced it, (2) the year it was introduced, (3) who developed its modern sense, (4) the title of the influential ethnographic book, and (5) which literary criticism movement employs it.
Give a brief overview of thick description.
Gilbert Ryle introduced thick description in 1968, and Clifford Geertz later developed its modern sense in The Interpretation of Cultures, influencing New Historicism."
23,646
Anthropology
High-altitude adaptation in humans
https://en.wikipedia.org/wiki/High-altitude_adaptation_in_humans
What is the altitude threshold for high-altitude adaptation?
Above 2,500 meters (8,200 ft)
What percentage of the global population lives above 2,500 meters?
Approximately 1.1%
Which evolutionary mechanism underlies high-altitude adaptation?
Natural selection
Which population exhibits the fastest known high-altitude adaptation?
Tibetans
When did Tibetan high-altitude adaptation occur?
Between 1,000 BCE and 7,000 BCE
Discuss high-altitude adaptation by addressing: (1) what is the altitude threshold for adaptation, (2) what percentage of the global population lives above 2,500 meters, (3) which evolutionary mechanism underlies this adaptation, (4) which population exhibits the fastest known adaptation, and (5) when did Tibetan high-altitude adaptation occur?
Summarize key facts about high-altitude adaptation in humans
Humans live above 2,500 meters (8,200 ft), representing about 1.1% of the global population; this adaptation is driven by natural selection, with Tibetans exhibiting the fastest known example between 1,000 BCE and 7,000 BCE"
20,933
Anthropology
Fictive kinship
https://en.wikipedia.org/wiki/Fictive_kinship
Which kinship ties does fictive kinship not rely on?
Consanguineal and affinal ties
What does fictive kinship contrast with?
True kinship ties
Until when was the term fictive kinship common?
Mid-to-late twentieth century
In legal contexts, in what matter is fictive kinship used?
Inheritance
What presumption underpins the cross-cultural validity of fictive kinship?
True kinship is cross-culturally valid
Discuss fictive kinship by addressing: (1) which kinship ties it does not rely on, (2) what it contrasts with, (3) until when it was commonly used, (4) its use in legal matters of inheritance, and (5) the presumption underlying its cross-cultural validity.
Summarize the concept of fictive kinship.
Fictive kinship does not rely on consanguineal and affinal ties, contrasting with true kinship ties. It was common until the mid-to-late twentieth century and is used in legal matters such as inheritance, resting on the presumption that true kinship is cross-culturally valid."
20,675
Anthropology
Dual inheritance theory
https://en.wikipedia.org/wiki/Dual_inheritance_theory
When was Dual Inheritance Theory developed?
1960s to early 1980s
What two evolutionary processes explain human behavior in DIT?
Genetic evolution and cultural evolution
How is 'culture' defined in Dual Inheritance Theory?
Socially learned behavior
What is the simplest form of social learning?
Blind copying of behaviors
Through what process does culture partly evolve in DIT?
Darwinian selection process
Discuss Dual Inheritance Theory by addressing: (1) when it was developed, (2) the two evolutionary processes it proposes, (3) how culture is defined, (4) the simplest form of social learning, and (5) how culture partly evolves.
Summarize the key aspects of Dual Inheritance Theory.
Dual Inheritance Theory emerged in the 1960s to early 1980s, positing that human behavior is shaped by genetic evolution and cultural evolution; it defines culture as socially learned behavior, notes that social learning involves blind copying of behaviors, and asserts that culture partly evolves through a Darwinian selection process."
15,176
Anthropology
Exocannibalism
https://en.wikipedia.org/wiki/Exocannibalism
What is exocannibalism?
Eating flesh of humans outside one's social group
What effect does exocannibalism aim to impose on its victims?
Ultimate humiliation and domination
Which culture in Mexico is documented as practicing exocannibalism?
Aztecs
How is exocannibalism alternatively interpreted besides a ritual act?
Form of predation
Which archaeologist linked resource scarcity with exocannibalism?
John Kantner
Discuss exocannibalism by addressing: (1) its definition, (2) the effect it imposes on victims, (3) which Mexican culture practiced it, (4) its alternative interpretation, and (5) the archaeologist who linked resource scarcity to it
Summarize the key aspects of exocannibalism
Exocannibalism is defined as eating the flesh of humans outside one's social group, intended to impose ultimate humiliation and domination; it was practiced by the Aztecs, is viewed as a form of predation, and was linked to resource scarcity by John Kantner"
13,069
Anthropology
Urban revolution
https://en.wikipedia.org/wiki/Urban_revolution
What process transforms small, kin-based, illiterate agricultural villages into urban societies?
urban revolution
Who introduced the term 'urban revolution'?
V. Gordon Childe
Which term did Childe coin for the transition from hunting-gathering to farming?
Neolithic Revolution
In what year was the book 'Man Makes Himself' published?
1936
What did Childe present in his 1950 article?
10-point model
Discuss the urban revolution by addressing: (1) the process that transforms small, kin-based, illiterate agricultural villages into urban societies, (2) who introduced the term 'urban revolution', (3) which coined term denotes the shift to farming, (4) when 'Man Makes Himself' was published, and (5) what model was presented in the 1950 article
Summarize the urban revolution concept
The urban revolution transformed small villages into urban societies, was introduced by V. Gordon Childe who coined Neolithic Revolution, first discussed in 1936 and later illustrated by a 10-point model"
12,884
Anthropology
Xenocentrism
https://en.wikipedia.org/wiki/Xenocentrism
What is xenocentrism?
Preference for other cultures' practices
Which 18th-century movement romanticized the noble savage?
Primitivism
Who coined the term xenocentrism?
Donald P. Kent and Robert G. Burnight
Which US political party exemplified xenocentrism through its opposition to native politics?
Communist Party USA
Which term contrasts with xenocentrism by valuing one's own culture?
Ethnocentrism
Discuss xenocentrism by addressing: (1) its definition, (2) the movement that romanticized the noble savage, (3) the sociologists who coined the term, (4) the political party reflecting this attitude, and (5) its contrasting term
Give a brief overview of xenocentrism
Xenocentrism is the preference for other cultures' practices, exemplified by the primitivism movement's romanticization of the noble savage. It was coined by Donald P. Kent and Robert G. Burnight and is reflected in the actions of the Communist Party USA, standing in contrast to ethnocentrism."
11,900
Anthropology
Tholu bommalata
https://en.wikipedia.org/wiki/Tholu_bommalata
Which Indian state is known for the Tholu bommalata tradition?
Andhra Pradesh
To which historical period do the origins of Tholu bommalata trace back?
3rd century BCE
What type of patronage has Tholu bommalata historically received?
Consistent royal patronage
Which Indonesian puppet theatre evolved from Tholu bommalata?
Wayang
What is the literal translation of 'Tholu bommalata'?
The dance of leather puppets
Discuss Tholu bommalata by addressing: (1) which Indian state is associated with it, (2) when its origins began, (3) what kind of patronage it received, (4) which Indonesian puppet theatre evolved from it, and (5) its literal translation.
Provide a brief overview of Tholu bommalata.
Originating in Andhra Pradesh during the 3rd century BCE, Tholu bommalata enjoyed consistent royal patronage and is the ancestor of Wayang, with its name literally meaning the dance of leather puppets."
10,383
Anthropology
Political anthropology
https://en.wikipedia.org/wiki/Political_anthropology
What does political anthropology study?
Politics in historical, social, and cultural settings
From which century does political anthropology originate?
19th century
Whose scientific approach influenced early political anthropology?
Charles Darwin
What key concept did early political anthropology emphasize?
Kinship
What was the goal of taxonomy in political anthropology?
Classify societies into discrete categories
Discuss political anthropology by addressing: (1) What does political anthropology study?, (2) From which century does it originate?, (3) Whose scientific approach influenced it?, (4) What key concept did it emphasize?, and (5) What was the goal of taxonomy in political anthropology?
Summarize the foundations of political anthropology
Political anthropology studies politics in historical, social, and cultural settings; it originated in the 19th century, was influenced by Charles Darwin, emphasized kinship, and used taxonomy to classify societies into discrete categories"
8,982
Anthropology
Feminist anthropology
https://en.wikipedia.org/wiki/Feminist_anthropology
What approach does feminist anthropology use?
A four-field approach. Multifaceted.
When was feminist anthropology formally recognized?
1970s
What defunct journal is associated with feminist anthropology?
Voices
What association was established for feminist anthropology?
Association for Feminist Anthropology
Who authored the ethnography 'The House of Lim'?
Margery Wolf
Discuss feminist anthropology by addressing: (1) what approach it uses, (2) when it was formally recognized, (3) which defunct journal is associated with it, (4) what association was established for it, and (5) who authored 'The House of Lim'?
Summarize key aspects of feminist anthropology.
Feminist anthropology employs a four-field approach, was formally recognized in the 1970s, had a defunct journal called Voices, established the Association for Feminist Anthropology, and featured Margery Wolf, author of 'The House of Lim'."
6,960
Anthropology
Biocultural anthropology
https://en.wikipedia.org/wiki/Biocultural_anthropology
What does biocultural anthropology study?
Relationships between human biology and culture
When did physical anthropologists view biology-culture differences racially?
First half of the 20th century
What theory emerged in the 1960s from exploring culture's role in human biology?
Dual inheritance theory
What concept was introduced in the 1970s following Dual inheritance theory?
Biocultural evolution
Who conducted early biocultural research in 1958?
Frank B. Livingstone
Discuss biocultural anthropology by addressing: (1) what it studies, (2) when physical anthropologists viewed these differences racially, (3) the theory developed in the 1960s, (4) the concept introduced in the 1970s, and (5) which anthropologist conducted key research in 1958.
Summarize key milestones in biocultural anthropology.
Biocultural anthropology examines relationships between human biology and culture; early 20th-century researchers viewed these differences racially, leading to Dual inheritance theory in the 1960s, biocultural evolution in the 1970s, and seminal research by Frank B. Livingstone in 1958."
6,755
Anthropology
Nesher Ramla Homo
https://en.wikipedia.org/wiki/Nesher_Ramla_Homo
Which extinct archaic human group lived during the Middle Pleistocene in Israel?
Nesher Ramla Homo group
In what year was tool industry evidence discovered at Nesher Ramla?
2010
When was the first Nesher Ramla Homo individual identified?
2021
In what type of landform was the Nesher Ramla site discovered?
Karst depression
What dating range was assigned to the Nesher Ramla remains?
140–120 kya
Discuss the Nesher Ramla Homo group by addressing: (1) which archaic human group lived during the Middle Pleistocene in Israel, (2) the year tool industry evidence was discovered, (3) when the first individual was identified, (4) the type of landform where the site was discovered, and (5) the dating range of the remains.
Summarize the key findings on the Nesher Ramla Homo discovery.
The Nesher Ramla Homo group was evidenced in 2010 and identified in 2021 at a site discovered in a karst depression, with remains dated to 140–120 kya."
6,657
Anthropology
Conflict continuum
https://en.wikipedia.org/wiki/Conflict_continuum
What is the highest intensity condition on the conflict continuum?
Explosiveness.
What outcome did the original game theory model propose?
A winner and a loser in a zero-sum game.
What term describes a deadlock between antagonists?
Standoff.
Who identified a continuum within competition in 2018?
Kelly McCoy.
Who cautioned that the gray zone must not blur peace and war in 2020?
Donald Stoker and Craig Whiteside.
Discuss the conflict continuum by addressing: (1) the highest intensity condition, (2) the original game theory outcome, (3) the term for antagonistic deadlock, (4) the identification of a competition continuum in 2018, and (5) the 2020 caution regarding the gray zone.
Summarize key aspects of conflict continuum and strategic cautions.
The conflict continuum culminates in explosiveness. The original game theory model proposed a winner and a loser in a zero-sum game. Standoff denotes a deadlock between antagonists. Kelly McCoy identified a competition continuum, while Donald Stoker and Craig Whiteside cautioned about the gray zone blurring peace and war."
6,510
Applied sciences
Kinesiology
https://en.wikipedia.org/wiki/Kinesiology
What does kinesiology study?
Human body movement
What degree in kinesiology prepares for graduate study?
Bachelor's degree
Which country licenses kinesiologists?
Canada
What system is used for measuring human motion?
Motion tracking systems
What method studies muscle and brain activity?
Electrophysiology
Discuss kinesiology by addressing: (1) its focus on human body movement, (2) the degree preparation for graduate study, (3) the country licensing kinesiologists, (4) the system used for measuring human motion, and (5) the method used to study muscle and brain activity.
Provide a brief overview of kinesiology
Kinesiology focuses on human body movement, involves a bachelor's degree for advanced study, is uniquely licensed in Canada, and utilizes motion tracking systems along with electrophysiology to study muscle and brain activity"
252,039
Applied sciences
Home economics
https://en.wikipedia.org/wiki/Home_economics
When did home economics begin in Scotland?
1850s
What was the lead skill taught in early home economics courses in Scotland?
Sewing
Which organization promoted vocational skills for youth in early 20th century America?
American Association of Family and Consumer Sciences
In what broader subject is family and consumer science now included?
Career Technical Education
What trend has been observed in home economics course offerings?
Major decline in home economics courses
Discuss the evolution of home economics by addressing: (1) when it began in Scotland, (2) the lead skill taught, (3) the organization that promoted youth vocational skills, (4) the broader subject it is now included in, and (5) the trend in its course offerings
Summarize the evolution of home economics education
Home economics began in the 1850s with sewing as its lead skill, the American Association of Family and Consumer Sciences promoted vocational skills, it is now part of Career Technical Education, and there has been a major decline in home economics courses"
73,621
Applied sciences
Agronomy
https://en.wikipedia.org/wiki/Agronomy
What are agronomy professionals called?
Agronomists
When did early humans begin domesticating plants such as wheat, barley, and rice?
10,000 BCE
Which 12th-century Andalusian agronomist authored Kitāb al-Filāḥa?
Ibn al-'Awwam
Which German chemist revealed that plants require essential minerals?
Justus von Liebig
In which century did agronomy become a distinct scientific discipline?
1800s
Discuss agronomy by addressing: (1) what agronomy professionals are called, (2) when early human plant domestication began, (3) which 12th-century Andalusian agronomist authored Kitāb al-Filāḥa, (4) which German chemist revealed the need for essential minerals in plants, and (5) in which century agronomy emerged as a distinct scientific discipline.
Provide a brief history of agronomy.
Agronomists are the specialists in a field that began with plant domestication around 10,000 BCE, marked by contributions from Ibn al-'Awwam and Justus von Liebig, and culminating in agronomy's emergence as a distinct discipline in the 1800s."
70,546
Applied sciences
Applied science
https://en.wikipedia.org/wiki/Applied_science
What branch does food science belong to?
Applied science
Which applied science field applies statistics and probability theory?
Genetic epidemiology
What does basic science focus on?
Advancing scientific theories and laws
For what purpose does applied research collect data?
Practical purposes
In geographical research, what does applied research utilize?
Existing geographical theories and methods
Discuss the practical application of scientific knowledge by addressing: (1) what branch food science belongs to, (2) which applied science field applies statistics and probability theory, (3) what basic science focuses on, (4) for what purpose applied research collects data, and (5) what applied research utilizes in geographical research
Summarize the practical application of scientific knowledge
Food science is part of applied science, exemplified by genetic epidemiology; basic science focuses on advancing scientific theories and laws, while applied research addresses practical purposes using existing geographical theories and methods"
65,351
Applied sciences
Human nutrition
https://en.wikipedia.org/wiki/Human_nutrition
Give an example of mineral nutrients.
Magnesium, Calcium, zinc, potassium, sodium, phosphorus
When were the first Recommended Dietary Allowances published?
1943
Which board deems nutrient levels sufficient for the RDAs?
Food and Nutrition Board.
What is the current edition of the Recommended Dietary Allowances?
Tenth edition.
What is essential for children’s physical and mental development?
Good nutrition.
Discuss human nutrition and RDAs by addressing: (1) which mineral is cited as an example of a nutrient, (2) when the first Recommended Dietary Allowances were published, (3) which board deems nutrient levels sufficient for the RDAs, (4) what is the current edition of the Recommended Dietary Allowances, and (5) what is essential for children’s physical and mental development.
Summarize key aspects of human nutrition and Recommended Dietary Allowances.
Magnesium is highlighted as an example nutrient; the first RDAs were published in 1943, the Food and Nutrition Board sets these standards in the tenth edition, and good nutrition is essential for children’s physical and mental development."
52,654
Applied sciences
Food science
https://en.wikipedia.org/wiki/Food_science
What is an alternative name for food science?
Bromatology
Which subdiscipline studies chemical interactions in foods?
Food chemistry
Which organization defined food science using multiple sciences?
Institute of Food Technologists
Which engineering field contributes to food technology?
Chemical engineering
What evaluation method assesses food taste using survey panels?
Sensory evaluation
Discuss food science by addressing: (1) its alternative name, (2) the subdiscipline studying chemical interactions in foods, (3) the organization defining it using multiple sciences, (4) the engineering field contributing to food technology, and (5) the evaluation method for assessing food taste.
Provide a brief overview of food science.
Food science, also known as bromatology, includes food chemistry, is defined by the Institute of Food Technologists, benefits from chemical engineering concepts, and utilizes sensory evaluation for assessing food taste."
39,826
Applied sciences
Criminal investigation
https://en.wikipedia.org/wiki/Criminal_investigation
What do collected facts in a criminal investigation inform?
criminal trials
What is the collective term for modern scientific techniques used in investigations?
forensic science
What right is granted to both the accuser and accused in the Code of Hammurabi?
to present evidence
Who was an early recorded professional criminal investigator?
the English constable
Which organizations most commonly conduct modern criminal investigations?
government police forces
Discuss criminal investigation by addressing: (1) what collected facts inform, (2) the term for modern scientific techniques, (3) the right granted in the Code of Hammurabi, (4) the early recorded professional investigator, and (5) which organizations conduct investigations
Summarize key aspects of criminal investigation
Collected facts inform criminal trials, modern techniques are known as forensic science, the Code of Hammurabi granted the right to present evidence, early investigation is exemplified by the English constable, and government police forces conduct investigations"
39,399
Applied sciences
Sports science
https://en.wikipedia.org/wiki/Sports_science
From which ancient civilization does sports science trace its origins?
Ancient Greece
Which ancient Greek physician wrote essays on health improvement?
Galen
How many essays did Galen write?
87
Which invention in the 15th century facilitated the spread of anatomical ideas?
Gutenberg's printing press
What early American medical school, formed in 1782, is cited for sports science?
Harvard Medical School
Discuss sports science by addressing: (1) its origins in Ancient Greece, (2) the physician who wrote health essays, (3) the number of essays he wrote, (4) the invention that spread anatomical ideas, and (5) the early American medical school cited for sports science.
Summarize key historical milestones in sports science
Sports science originated in Ancient Greece, with Galen writing 87 essays, spread through Gutenberg's printing press, and exemplified by Harvard Medical School."
27,533
Applied sciences
Applied economics
https://en.wikipedia.org/wiki/Applied_economics
What is applied economics?
Application of economic theory and econometrics in specific settings
What is the purpose of applied economics for economic development?
Enhance business practices and national policy making
What process does applied economics involve regarding core theory?
Reduction in abstraction of core theory
What alternative label is used for applied economics by one source?
The art of economics
Which two economists are noted in the origins of applied economics?
Say and Mill
Discuss applied economics by addressing: (1) what it is, (2) its purpose for economic development, (3) the process involving abstraction reduction, (4) the alternative label used, and (5) the two economists noted in its origins
Give a brief overview of applied economics
Applied economics applies economic theory and econometrics in specific settings to enhance business practices and national policy making, involves reduction in abstraction of core theory, is termed the art of economics, and originates from Say and Mill"
17,767
Applied sciences
Outline of applied science
https://en.wikipedia.org/wiki/Outline_of_applied_science
What is applied science?
Developing practical applications using scientific knowledge
Which field applies mathematical and statistical methods to assess risk?
Actuarial science
What does agronomy study?
Producing and using plants
What does aquaculture involve?
Farming aquatic organisms
What is olericulture?
Vegetable growing
Discuss applied science by covering: (1) what applied science is, (2) which field applies mathematical and statistical methods to assess risk, (3) what agronomy studies, (4) what aquaculture involves, and (5) what olericulture is
Summarize key branches of applied science
Applied science involves developing practical applications using scientific knowledge, with actuarial science as one field, agronomy focused on producing and using plants, aquaculture involving farming aquatic organisms, and olericulture centered on vegetable growing"
15,581
Applied sciences
Nanoelectromechanical systems
https://en.wikipedia.org/wiki/Nanoelectromechanical_systems
What precision does the SiTime SiT8008 achieve?
Quartz precision
Where are the nanoscale transistors and mechanical components integrated?
Same chip package
What functionalities do NEMS integrate?
Electrical and mechanical
From which systems do NEMS evolve?
MEMS devices
Which quantum mechanical effect is notable in NEMS?
Zero point motion
Discuss nanoscale functionality by addressing: (1) the precision of the SiTime SiT8008, (2) where the nanoscale transistors and mechanical components are integrated, (3) the functionalities integrated in NEMS, (4) the predecessor systems of NEMS, and (5) the notable quantum mechanical effect in NEMS.
Provide a brief overview of nanoscale device functionality and NEMS.
The SiTime SiT8008 achieves quartz precision with its nanoscale transistors and mechanical components on the same chip package. NEMS integrate electrical and mechanical functionalities, evolve from MEMS devices, and exhibit zero point motion."
10,805
Applied sciences
Applied anthropology
https://en.wikipedia.org/wiki/Applied_anthropology
What is applied anthropology?
Practical application of anthropological theories, methods, and practices.
Who first proposed the term applied anthropology?
Daniel G. Brinton.
How did John Van Willengen define applied anthropology?
Anthropology put to use.
How many subareas does anthropology encompass?
Four.
Which organization's website describes anthropology as the study of humans?
American Anthropological Association.
Discuss applied anthropology by addressing: (1) What is applied anthropology?, (2) Who first proposed the term applied anthropology?, (3) How did John Van Willengen define applied anthropology?, (4) How many subareas does anthropology encompass?, and (5) Which organization's website describes anthropology as the study of humans?
Summarize the key aspects of applied anthropology.
Applied anthropology is the practical application of anthropological theories, methods, and practices, associated with Daniel G. Brinton and described as anthropology put to use; it comprises four subareas as recognized by the American Anthropological Association."
7,554
Applied sciences
Artes mechanicae
https://en.wikipedia.org/wiki/Artes_mechanicae
What medieval term denotes ordered practical skills?
Artes mechanicae
Which 9th-century scholar divided the mechanical arts into seven parts?
Johannes Scotus Eriugena
How many parts did Johannes Scotus Eriugena define?
Seven
Which 12th-century scholar introduced an applied geometry classification for these skills?
Dominicus Gundissalinus
Which subjects did Hugh of St Victor include in his Didascalicon instead of commerce, agriculture, and cooking?
Navigation, medicine, theatrical arts
Discuss medieval practical skills by addressing: (1) what term denotes ordered practical skills, (2) which 9th-century scholar divided the mechanical arts into seven parts, (3) how many parts did he define, (4) which 12th-century scholar introduced applied geometry, and (5) which subjects did Hugh of St Victor include in his Didascalicon instead of commerce, agriculture, and cooking?
Provide a brief overview of medieval practical skills and their classifications
Artes mechanicae define medieval practical skills, divided into seven parts by Johannes Scotus Eriugena, later classified by Dominicus Gundissalinus, with Hugh of St Victor including navigation, medicine, and theatrical arts"
6,818
Artificial intelligence
Artificial intelligence
https://en.wikipedia.org/wiki/Artificial_intelligence
What capability does artificial intelligence refer to?
Performing tasks associated with human intelligence
In which field is artificial intelligence research conducted?
Computer science
What are machines with artificial intelligence called?
AIs
Which company is given as an example of autonomous vehicles?
Waymo. Tesla.
What long-term goal of AI research is specified?
General intelligence
Discuss artificial intelligence by addressing: (1) what capability it refers to, (2) the research field it is studied in, (3) what machines with AI are called, (4) which autonomous vehicle example is given, and (5) what its long-term research goal is
Provide a brief overview of artificial intelligence
Artificial intelligence involves performing tasks associated with human intelligence and is researched in computer science; machines with this ability are called AIs, with Waymo cited as an autonomous vehicle example, and achieving general intelligence is a long-term goal."
3,754,923
Artificial intelligence
Artificial general intelligence
https://en.wikipedia.org/wiki/Artificial_general_intelligence
What is AGI intended to achieve relative to human abilities?
Match or surpass human capabilities
How is artificial superintelligence defined?
AGI that greatly exceeds human capabilities
What is the primary goal of companies like OpenAI in AI research?
Creating AGI
How many active AGI research projects were identified in 2020?
72 active projects
Which AI researcher expressed concerns about AGI's rapid progress?
Geoffrey Hinton. Yann Lecun, Yoshua Bengio.
Discuss AGI by addressing: (1) its intended achievement relative to human abilities, (2) the definition of artificial superintelligence, (3) the primary goal of companies like OpenAI, (4) the number of active AGI research projects in 2020, and (5) the AI researcher who expressed concerns
Summarize key aspects of AGI research
AGI is intended to match or surpass human capabilities, while artificial superintelligence is defined as AGI that greatly exceeds them; creating AGI is the main goal supported by 72 active projects and concerns voiced by Geoffrey Hinton"
555,609
Artificial intelligence
Intelligent agent
https://en.wikipedia.org/wiki/Intelligent_agent
What does an intelligent agent perceive?
Its environment
What behavior is central to intelligence?
Goal-directed behavior
What encapsulates an intelligent agent's goals?
Objective function
What function shapes a reinforcement learning agent's behavior?
Reward function
What function guides an evolutionary algorithm's behavior?
Fitness function
Discuss intelligent agents by addressing: (1) What does an intelligent agent perceive?, (2) What behavior is central to intelligence?, (3) What encapsulates an intelligent agent's goals?, (4) What function shapes a reinforcement learning agent's behavior?, and (5) What function guides an evolutionary algorithm's behavior?
Summarize the core functions of intelligent agents.
An intelligent agent perceives its environment, exhibits goal-directed behavior, operates with an objective function, employs a reward function, and uses a fitness function"
145,798
End of preview. Expand in Data Studio

SLAQ: Short-Long Form Alignment for Factual Question Answering

This repository hosts the Short-Long Form Alignment for Factual Question Answering (SLAQ) dataset and associated resources from the paper "The Curious Case of Factual (Mis)Alignment between LLMs' Short- and Long-Form Answers".

SLAQ is a controlled evaluation framework designed to compare Large Language Models (LLMs)' factual answers when questions are asked (a) in isolation (short-form) versus (b) integrated into complex queries (long-form). This benchmark aims to assess the factual consistency and trustworthiness of LLMs across varying query complexities.

Paper: The Curious Case of Factual (Mis)Alignment between LLMs' Short- and Long-Form Answers Code: https://github.com/WorldHellow/SLAQ

framework

Results

The image below provides SLAQ factual accuracy and alignment scores for Gemma, Qwen and Llama models. You can go over these results in the evaluation/raw_benchmarking_results folder.

scores

Citation

If you find this dataset or framework useful for your research, please consider citing the paper:

@misc{islam2025curiouscasefactualmisalignment,
      title={The Curious Case of Factual (Mis)Alignment between LLMs' Short- and Long-Form Answers}, 
      author={Saad Obaid ul Islam and Anne Lauscher and Goran Glavaš},
      year={2025},
      eprint={2510.11218},
      archivePrefix={arXiv},
      primaryClass={cs.CL},
      url={https://arxiv.org/abs/2510.11218}, 
}
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