Current Events and History

Antarctica

Flag	Country	Capital	Notes
	Bouvet Island	—	Overseas territory of Norway
	French Southern Territories[Antarctica 1]	—	Overseas territory of France
	Heard Island and McDonald Islands	—	Overseas territory of Australia

Asia is home to seven of the world's twelve longest rivers, but its waterways are also of high cultural, spiritual, and economic importance. Here are the ten Asian rivers that every quiz bowl team should be familiar with.

1. 
   The Yangtze (or Chang Jiang or Ch'ang Chiang) is the longest river in China and Asia and the third longest in the world. It rises in the Kunlun Mountains, flows across the Tibetan Plateau, passes the cities of Chongqing, Wuhan, Nanjing, and Shanghai, and empties into the South China Sea. Its basin is China's granary and is home to nearly one in every three Chinese citizens. The river has been in the news for the construction of the Three Gorges Dam, the world's largest, which will reduce flooding but displace 1.5 million people and bury more than 1,300 known archaeological sites.
   
2. 
   The Brahmaputra (or Tsangpo or Jamuna) runs 1,800 miles from its source in the Tibetan Himalayas; it starts eastward across the plateau, then turns south into the Indian state of Assam, and then enters Bangladesh where it merges with the Ganges to form the world's largest delta. While serving as a historical route to Tibet, the river is also prone to disastrous flooding.
   
3. 
   The Yellow River (or Huang He or Huang Ho) is, at 3,400 miles, China's second-longest; it is also the most important to the northern half of the country. It rises in Qinghai province and flows into the Bohai Gulf of the Yellow Sea. The river's name comes from the extraordinary amount of loess silt that it carries, an average of 57 pounds for every cubic yard of water. Among its notable features is the Grand Canal, built during the Ming Dynasty, that links it to the Yangtze.
   
4. 
   The Ganges (or Ganga) is the holiest river of Hinduism. It rises in the Himalayas and flows a comparatively short 1,560 miles to the world's largest delta on the Bay of Bengal. Among that delta's distributaries are the Hooghly (on whose banks Kolkata (formerly Calcutta) may be found) and the Padma (which enters Bangladesh). Approximately one in every twelve human beings lives in the Ganges Basin, a population density that is rapidly polluting the river; a significant source of that pollution is cremated remains.
   
5. 
   The Mekong is the chief river of Southeast Asia. It originates in eastern Tibet, forms much of the Laos-Thailand border, flows south through Cambodia, and enters the South China Sea in southern Vietnam just south of Ho Chi Minh City. The capital cities of Vientiane and Phnom Penh are on the Mekong. The building of dams and clearing of rapids are a source of diplomatic conflict between China, Laos, and Cambodia.
   
6. 
   The Tigris is the eastern of the two rivers that define the historic region of Mesopotamia (meaning, "The Land Between Two Rivers") that was home to the ancient civilizations of Sumer and Akkad. It rises in Turkey, then flows southeast by Mosul, Tikrit, and Baghdad before joining the Euphrates to make the Shatt-al-Arab, which subsequently empties into the Persian Gulf.
   
7. 
   The Euphrates defines the western border of Mesopotamia; it also rises in the Zagros Mountains of Turkey and its shores are home to Fallujah and Babylon. It is the longer of the two rivers with a course of 1,740 miles (compared to the Tigris' 1,180). Both the Tigris and the Euphrates have changed courses several times leaving ruins in the desert where cities have been abandoned.
   
8. 
   The Irrawaddy (or Ayeyarwaddy) is the chief river of Myanmar (also known as Burma). It flows 1,350 miles past Yangon (formerly Rangoon) and Mandalay to the Gulf of Martaban, an arm of the Bay of Bengal. Its delta is one of the world's most important rice-growing regions, and its name is thought to come from the Sanskrit word for "elephant."
   
9. 
   The Indus is the chief river of Pakistan as well as being the ultimate source of the name of India. It rises in Tibet and flows 1,800 miles to a delta on the Arabian Sea southeast of Karachi. The five major tributaries of the Indus, the Jhelum, Chenab, Ravi, Beas, and Sutlej Rivers, are the source of the name of the Punjab region, which is Persian for "Land of the Five Rivers". The Indus is the cradle of the Indus Valley Civilization, one of the world's earliest urban areas, whose main cities were Mohenjo-Daro and Harappa.
   
10. 
    The Jordan River rises in Syria from springs near Mount Hermon. It flows south to Lake Merom, through the Sea of Galilee, and into the Dead Sea, which lies 1,300 feet below sea level. The river forms the nation of Jordan's boundary with the West Bank and northern Israel. In the New Testament, the river was the site of the baptism of John the Baptist. In modern times, about 80% of its water is diverted for human use, a figure that has led to the shrinking of the Dead Sea and serious contention among bordering nations.
    

You can also look at www.artchive.com – you should know all these artists!

Below is a list of ten paintings which are frequent quiz bowl topics. This list focuses on individual paintings rather than bodies of work; thus, an artist like Georgia O'Keeffe is not included because no specific one of her familiar cowskull-and-flower paintings is sufficiently prominent. The list is notably skewed toward the first half of the 20th century, as only one work was painted after 1950. Perhaps the earlier paintings have simply had more time to be influential and make their way into the artistic canon. Also, many prominent post-1950 painters, like Jackson Pollock and Mark Rothko, do not have a specific work with a catchy title that has gained particular attention above all others; like O'Keeffe, they are known for their style and collective body of work rather than for any one painting.

1. 
   Guernica, by Pablo Picasso. Guernica was a Basque town bombed by the Germans during the Spanish Civil War in April 1937. Picasso had already been commissioned to paint a mural for the Spanish Pavilion at the World's Fair, and he completed his massive, black, white, and grey anti-war mural by early June 1937. Picasso's Cubist approach to portraying the figures adds to the sense of destruction and chaos. Guernica was in the Museum of Modern Art (MOMA) in New York until 1981, when it was returned to the Museo Nacional Centro de Arte Reina Sofia in Spain.
   
2. 
   Nude Descending a Staircase, No. 2, by Marcel Duchamp. First painted in 1912, Nude Descending a Staircase created a sensation when shown at the 1913 Armory Show in New York, where one critic referred to it as "an explosion in a shingle factory." Painted in various shades of brown, Nude Descending a Staircase portrays a nude woman in a series of broken planes, capturing motion down several steps in a single image. The painting reflects a Cubist sense of division of space, and its portrait of motion echoes the work of the Futurists.
   
3. 
   The Persistence of Memory, by Salvador Dalí. First shown in 1931, The Persistence of Memory is probably the most famous of surrealist paintings. The landscape of the scene echoes Port Lligat, Dalí's home. The ants, flies, clocks, and the Port Lligat landscape are motifs in many other Dalí paintings, and the trompe l'oeil depiction of figures is typical of his works. It currently belongs to MOMA; its 1951 companion piece, The Disintegration of the Persistence of Memory, hangs at the Salvador Dalí Museum in St. Petersburg, Florida.
   
4. 
   Les Demoiselles d'Avignon, by Pablo Picasso. This painting depicts five women in a brothel. However, the images of the women are partly broken into disjointed, angular facets. The degree of broken-ness is rather mild compared to later Cubist works, but it was revolutionary in 1907. The rather phallic fruit arrangement in the foreground reflects the influence of Cezanne's "flattening of the canvas." The two central figures face the viewer, while the other three have primitive masks as faces, reflecting another of Picasso's influences. It is currently housed at the MOMA.
   
5. 
   Broadway Boogie Woogie, by Piet Mondrian. While Les Demoiselles d'Avignon and other Cubist paintings represent an extension of Paul Cezanne's division-of-space approach to the canvas, Mondrian's De Stijl works are a still further abstraction, such that the canvas is often divided up into rectangular "tile patterns," as in Composition in Red, Yellow, and Blue. The painting simultaneously echoes the bright lights of a marquee, resembles a pattern of streets as seen from above, and creates a feeling of vitality and vibrancy, not unlike the music itself. This work can also be found at the MOMA.
   
6. 
   Campbell's Soup Can, by Andy Warhol. Pop Art parodies (or perhaps reflects) a world in which celebrities, brand names, and media images have replaced the sacred; Warhol's series of Campbell's Soup paintings may be the best illustration of this. Like the object itself, the paintings were often done by the mass-produceable form of serigraphy (silk screening). Also like the subject, the Warhol soup can painting existed in many varieties, with different types of Campbell's Soup or numbers of cans; painting 32 or 100 or 200 identical cans further emphasized the aspect of mass production aspect in the work. The same approach underlies Warhol's familiar series of prints of Marilyn Monroe, Jacqueline Kennedy Onassis, and other pop culture figures.
   
7. 
   Nighthawks, by Edward Hopper. As is often the case with his works, Hopper uses a realistic approach (including such details as the fluorescent light of the diner, the coffee pots, and the Phillies cigar sign atop the diner) to convey a sense of a loneliness and isolation, even going so far as to depict the corner store without a door connecting to the larger world. Hopper's wife Jo served as the model for the woman at the bar. Nighthawks is housed at the Art Institute of Chicago.
   
8. 
   I and the Village, by Marc Chagall. Painted in 1911, I and the Village is among Chagall's earliest surviving paintings. It is a dreamlike scene which includes many motifs common to Chagall, notably the lamb and peasant life. In addition to the two giant faces—a green face on the right and a lamb's head on the left—other images include a milkmaid, a reaper, an upside-down peasant woman, a church, and a series of houses, some of them upside-down. I and the Village is currently housed at MOMA.
   
9. 
   Christina's World, by Andrew Wyeth. The Christina of the title is Christina Olson, who lived near the Wyeths' summer home in Cushing, Maine. In the 1948 painting, Christina lays in the cornfield wearing a pink dress, facing away from the viewer, her body partly twisted and hair blowing slightly in the wind. In the far distance is a three-story farmhouse with dual chimneys and two dormers, along with two sheds to its right. A distant barn is near the top middle of the painting. One notable aspect is the subtle pattern of sunlight, which strikes the farmhouse obliquely from the right, shines in the wheel tracks in the upper right, and casts very realistic-looking shadows on Christina's dress. The Olson house was the subject of many Andrew Wyeth paintings for 30 years, and it was named to the National Register of Historic Places for its place in Christina's World.
   
10. 
    American Gothic, by Grant Wood. Wood painted his most famous work after a visit to Eldon, Iowa, when he saw a Carpenter Gothic style house with a distinctive Gothic window in its gable. Upon returning to his studio, he used his sister Nan and his dentist, Dr. Byron McKeeby, as the models for the two figures. The pitchfork and the clothing were more typical of 19th-century farmers than contemporary ones. American Gothic is among the most familiar regionalist paintings, and it is said to be the most parodied of all paintings. It hangs at the Art Institute of Chicago, where it was submitted for a competition by Wood upon its completion in 1930 (Wood won a bronze medal and a $300 prize).
    

The following table lists the thirty most-frequently referenced works of visual art in NAQT questions as of May 7, 2002. While you really gotta know their creators, these are also some of the works about which more substantive questions are written, so teams should be prepared for questions on their materials, design, technique, depicted action, and circumstances of creation.

1. 
   Frank Lloyd Wright (1867 - 1959) Wright's life and works are staples of quiz tournaments. Born in Wisconsin, he worked under Louis Sullivan before founding a Chicago practice. His early homes, like the Robie House at the University of Chicago, are in the "Prairie" style: horizontal orientation and low roofs. His "organic architecture" tries to harmonize with its inhabitants and site: Examples include the Kaufmann House (also known as Fallingwater) in Pennsylvania; the Johnson Wax Museum in Racine, Wisconsin; and Taliesin West, his Arizona home and studio. (The original Taliesin, in Wisconsin, burned down in 1914). Other notable Wright works are the Guggenheim Museum in New York City, the Larkin Building in Buffalo, the Unity Temple in Oak Park, and the Imperial Hotel in Tokyo, one of few buildings to survive a 1923 earthquake.
   
2. 
   Walter Gropius (1883 - 1969) Though Gropius also designed the Fagus Factory (Alfeld, Germany) and the Pan American Building (New York City), he is better known for founding the Bauhaus. Beginning in Weimer in 1919 and moving to a Gropius-designed facility in Dessau in 1925, the Bauhaus school emphasized functionalism, the application of modern methods and materials, and the synthesis of technology and art. Its faculty included artists Paul Klee, Wassily Kandinsky, and Josef Albers. Gropius would later head Harvard's architecture department from 1938-52, shifting its focus to incorporate modern design and construction techniques.
   
3. 
   Ludwig Mies van der Rohe (1886 - 1969) The leading architect of the International Style of skyscraper design, he (like Gropius) worked in the office of Peter Behrens. He directed the Bauhaus from 1930-33, shutting it down before the Nazis could do so. His works include the Barcelona Pavilion for the 1929 International Exposition; the Lake Shore Drive Apartments in Chicago; the New National Gallery in Berlin; and the Seagram Building in New York, which he co-designed with Philip Johnson. The phrase "less is more" is associated with Mies, whose glass-covered steel structures influenced the design of office buildings in nearly every major city in the U.S.
   
4. 
   I(eoh) M(ing) Pei (1917 - Present) Pei is among the most famous living architects. Born in China, he emigrated to the U.S. in 1935. Though he has also designed moderate-income housing, Pei is best known for large-scale projects. His works include the Mile High Center in Denver, the National Center for Atmospheric Research in Boulder, the John Hancock Building in Boston, the East Wing of the National Gallery of Art in Washington, D.C., the Fragrant Hill Hotel in Beijing, and the recent Miho Museum of Art in Shiga, Japan. He may be best known for two fairly recent works: the glass pyramid erected outside the Louvre in 1989, and the Rock and Roll Hall of Fame in Cleveland, Ohio, completed in 1995.
   
5. 
   Sir Christopher Wren (1632 - 1723) When fire destroyed much of London in 1666, Wren was an Oxford astronomy professor who had designed his first building just four years earlier. Charles II named him the King's Surveyor of Works in 1669, and he was involved in rebuilding more than 50 London churches in the next half-century, including Saint Paul's Cathedral. An inscription near his tomb in Saint Paul's declares, "Reader, if you seek a monument, look around you."
   
6. 
   Le Corbusier (born Charles-Eduoard Jeanneret) (1887 - 1965) Possibly more influential even than Wright, he wrote the 1923 book Towards a New Architecture, standard reading in architectural theory courses. One famous Corbusian quote is: "A house is a machine for living in." His floor plans were influenced by Cubist principles of division of space, and the Villa Savoye (Poissy, France) is his best-known early work. He wrote of the "Radiant City" begun anew, a completely planned city with skyscrapers for residents. Applications of his approach to government buildings (such as in Brasilia or in Chandigarh, India), however, largely failed, as did many urban renewal projects produced on the same ideological foundation. Nonetheless, he influenced every other 20th-century figure on this list.
   
7. 
   Louis Sullivan (1856 - 1924) Sullivan did not design the first skyscraper but did become a vocal champion of skyscrapers as reflections of the modern age. Though most associated with Chicago, his best-known work is the 1891 Wainwright Building in St. Louis. His partnership with Dankmar Adler produced over 100 buildings. Later works, such as the Babson, Bennett, and Bradley Houses, reflect an organic architecture distinct from that of Wright. Sullivan's dictum that "form should follow function" strongly influenced modern architecture; his writings helped break the profession from classical restraints.
   
8. 
   Filippo Brunelleschi (1377 - 1446) A friend of Donatello, Brunelleschi was a skilled sculptor and goldsmith whose 1401 competition with Lorenzo Ghiberti for the commission of the bronze doors of the Florence Baptistery is a frequent question topic (Ghiberti got the chief commission). As an architect, he is mainly known for the extraordinary octagonally-based dome of the Santa Maria del Fiore (also known as the Florence Cathedral), which dominates the Florentine skyline. The task required an innovative supporting framework and occupied much of his career (as described in detail in Vasari's Lives of the Artists). Other projects include the Spedale degli Innocenti (a hospital), the Old Sacristy at San Lorenzo, and the Pazzi Chapel in the Cloisters of Santa Croce, all from 1421 to 1430.
   
9. 
   Frank Gehry (1929 - Present) Winner of the 1989 Pritzker Prize, Gehry is best-known today for large-scale compositions like the Experience Music Project in Seattle, the Walt Disney Concert Hall in Los Angeles, and the recent, controversial Guggenheim Museum in Bilbao, Spain. (Bilbao natives describe the latter as "the artichoke," given its layers of abstract titanium structures.) Gehry often uses uncommon materials such as plywood and limestone; his designs range from Kobe's Fishdance Restaurant, shaped like a giant fish, to the soft-sculpture look of the so-called "Fred and Ginger" buildings in Prague. He also designs furniture: The Easy Edges line is made of laminated cardboard; the Gehry Collection consists of chairs named for hockey terms (e.g. Cross Check and Power Play). As of 2002, active projects included a new wing for the Corcoran Gallery and the SoHo Branch of the Guggenheim.
   
10. 
    Andrea Palladio (1508 - 1580) Born Andrea di Pietro della Gondola, Palladio designed villas in or near Venice, including the Villa Rotonda and Villa Barbaro. He integrated Greco-Roman ideas of hierarchy, proportion, and order with contemporary Renaissance styles. His Four Books on Architecture from 1570 relates his theoretical principles. Among architects heavily influenced by Palladio were Inigo Jones and Thomas Jefferson.
    
11. 
    Eero Saarinen (1910 - 1961) The son of architect Eliel Saarinen, Eero was born in Finland but spent most of his life in the U.S. and died in Ann Arbor, Michigan. He designed many buildings on the campuses of MIT and Yale, as well as Dulles International Airport and the TWA terminal at Kennedy Airport. Saarinen may be best known for designing the Gateway Arch in St. Louis, though he died before it was completed. Many of his works are characterized by elegant, sweeping forms, such as the Kresge Auditorium at MIT.
    
12. 
    Antonio Gaudi y Cornet (1852 - 1926) Gaudi created many extraordinary buildings in Barcelona in the early 20th century. His Art Nouveau-inspired works include the Casa Mila and Casa Batllo apartments, known from their undulating facades, and several works for patron Eusebi Guell. He spent 40 years working on the Expiatory Church of the Holy Family (also known as La Sagrada Familia); although its spindle-like towers are in place, the building remains unfinished, and Gaudi's models for it were destroyed in the Spanish Civil War. He was also fond of using hyperbolic paraboloids in his work.
    

The following table lists the 40 most-frequently referenced works of visual art in NAQT questions as of November 1, 2007. While you really gotta know their creators, these are also some of the works about which more substantive questions are written, so teams should be prepared for questions on their materials, design, technique, depicted action, and circumstances of creation.

1. 
   Michelangelo (1475 - 1564) A Florentine "Renaissance man" also known for architecture (the dome of St. Peter's Basilica), painting (The Last Judgment and the Sistine Chapel ceiling), poetry, and military engineering. His sculpted masterpieces include David, a Pietà, Bacchus, and a number of pieces for the tomb of Pope Julius II (including Dying Slave and Moses). He preferred to work in Carraran marble.
   
2. 
   Auguste Rodin (1840 - 1917) A French sculptor known for stormy relationships with "the establishment" of the École des Beaux-Arts [ay-kohl day boh-zar] and his mistress, fellow artist Camille Claudel. His works include The Age of Bronze, Honoré de Balzac, The Burghers of Calais, and a massive pair of doors for the Museum of Decorative Arts (the Gates of Hell) inspired by Dante's Inferno. That latter work included his most famous piece, The Thinker.
   
3. 
   Gian Lorenzo Bernini (1598 - 1680) A Roman who, with the rarely asked-about Francesco Borromini, defined the Baroque movement in sculpture. Bernini is principally known for his freestanding works including David and The Ecstasy of St. Theresa. Bernini's David differs from that of Michelangelo in that the hero is shown "in motion," having twisted his body to sling the rock. Bernini is also known for his massive fountains in Rome including the Triton and the Fountain of the Four Rivers.
   
4. 
   Donatello (1386 - 1466) A Florentine sculptor who helped define Renaissance sculpture as distinct from that of the Gothic period. He is known for St. Mark and St. George in the Or San Michele [OR SAHN mee-KAY-lay] (a Florentine church), the bald Zuccone (which means "pumpkin-head," though it depicts the prophet Habbakuk), and the first equestrian statue to be cast since Roman times, the Gattamelata in Padua. He is also known for mastering the low relief form of schiacciato.
   
5. 
   Lorenzo Ghiberti (1378 - 1455) A Florentine sculptor and goldsmith who taught both Donatello and Filippo Brunelleschi. He is best known for two pairs of bronze doors on the Florence Baptistery (associated with the Duomo, or Florentine Cathedral). He produced a single, low-relief panel to win a 1401 competition (defeating Brunelleschi) for the commission to design the 28 panels for the north doors. After that, he was given another commission to design ten panels for the east doors. This latter work, by far his most famous, was dubbed the "Gates of Paradise" by Michelangelo.
   
6. 
   Gutzon Borglum (1867 - 1941) An American known for crafting Mount Rushmore in the Black Hills of South Dakota. He is also known for The Mares of Diomedes and an unfinished (and later replaced) tribute to Confederate heroes on Stone Mountain in Georgia.
   
7. 
   Phidias (c. 480 BC - c. 430 BC) An Athenian considered the greatest of all Classical sculptors. He created the chryselephantine (gold and ivory) Statue of Zeus at Olympia (one of the Wonders of the Ancient World, now lost) and the statue of Athena in the Parthenon (now lost). He was supported by money from the Delian League (that is, the Athenian Empire) run by his friend Pericles; he was later ruined by charges of corruption generally considered to be part of a political campaign against Pericles.
   
8. 
   Constantin Brancusi (1876 - 1957) A Romanian sculptor who was a major figure in Modernism. He is best known for The Kiss (not to be confused with the Rodin work or the Klimt painting), Sleeping Muse, and Bird in Space. He's also the center of anecdote in which U.S. customs taxed his works as "industrial products" since they refused to recognize them as art.
   
9. 
   Daniel Chester French (1850 - 1931) An American who created The Minute Man for Concord, Massachusetts and Standing Lincoln for the Nebraska state capitol, but who is best known for the seated statue in the Lincoln Memorial.
   
10. 
    Frédéric-Auguste Bartholdi (1834-1904) A French sculptor primarily known as the creator of Liberty Enlightening the World, better known as the Statue of Liberty. He also executed The Lion of Belfort and a statue of the Marquis de Lafayette in New York's Union Square.
    

These are the ten people that have come up most frequently in NAQT's questions as a result of their accomplishments in pure mathematics.

1. 
   The work of Isaac Newton (1643-1727, English) in pure math includes generalizing the binomial theorem to non-integer exponents, doing the first rigorous manipulation with power series, and creating "Newton's method" for the finding roots. He is best known, however, for a lengthy feud between British and Continental mathematicians over whether he or Gottfried Leibniz invented calculus (whose differential aspect Newton called "the method of fluxions"). It is now generally accepted that they both did, independently.
   
2. 
   Euclid (c. 300 BC, Alexandrian Greek) is principally known for the Elements, a textbook on geometry and number theory, that was used for over 2,000 years and which grounds essentially all of what is taught in modern high school geometry classes. Euclid is known for his five postulates that define Euclidean (i.e., "normal") space, especially the fifth (the "parallel postulate") which can be broken to create spherical and hyperbolic geometries. He also proved the infinitude of prime numbers.
   
3. 
   Carl Friedrich Gauss (1777-1855, German) is considered the "Prince of Mathematicians" for his extraordinary contributions to every major branch of mathematics. His Disquisitiones Arithmeticae systematized number theory and stated the fundamental theorem of arithmetic. He also proved the fundamental theorem of algebra, the law of quadratic reciprocity, and the prime number theorem. Gauss may be most famous for the (possibly apocryphal) story of intuiting the formula for the summation of an arithmetic series when given the busywork task of adding the first 100 positive integers by his primary school teacher.
   
4. 
   Archimedes (287-212 BC, Syracusan Greek) is best known for his "Eureka moment" of using density considerations to determine the purity of a gold crown; nonetheless, he was the preeminent mathematician of ancient Greece. He found the ratios between the surface areas and volumes of a sphere and a circumscribed cylinder, accurately estimated pi, and presaged the summation of infinite series with his "method of exhaustion."
   
5. 
   Gottfried Leibniz (1646-1716, German) is known for his independent invention of calculus and the ensuing priority dispute with Isaac Newton. Most modern calculus notation, including the integral sign and the use of d to indicate a differential, originated with Leibniz. He also invented binary numbers and did fundamental work in establishing boolean algebra and symbolic logic.
   
6. 
   Pierre de Fermat (1601-1665, French) is remembered for his contributions to number theory including his "little theorem" that a^p will be divisible by p if p is prime. He also studied Fermat primes (those of the form 2²ⁿ+1) and stated his "Last Theorem" that xⁿ + yⁿ = zⁿ has no solutions if x, y, and z are positive integers and n is a positive integer greater than 2. He and Blaise Pascal founded probability theory. In addition, he discovered methods for finding the maxima and minima of functions and the areas under polynomials that anticipated calculus and inspired Isaac Newton.
   
7. 
   Leonhard Euler (1707-1783, Swiss) is known for his prolific output and the fact that he continued to produce seminal results even after going blind. He invented graph theory with the Seven Bridges of Königsberg problem and introduced the modern notation for e, the square root of -1 (i), and trigonometric functions. Richard Feynman called his proof that e^iπ = -1 "the most beautiful equation in mathematics" because it linked four of math's most important constants.
   
8. 
   Kurt Gödel (1906-1978, Austrian) was a logician best known for his two incompleteness theorems proving that every formal system that was powerful enough to express ordinary arithmetic must necessarily contain statements that were true, but which could not be proved within the system itself.
   
9. 
   Andrew Wiles (1953-present, British) is best known for proving the Taniyama-Shimura conjecture that all rational semi-stable elliptic curves are modular. This would normally be too abstruse to occur frequently in quiz bowl, but a corollary of that result established Fermat's Last Theorem.
   
10. 
    William Rowan Hamilton (1805-1865, Irish) is known for extending the notion of complex numbers to four dimensions by inventing the quaternions, a non-commutative field with six square roots of -1: ±i, ±j, and ±k with the property that ij = k, jk = i, and ki = j.
    

Physics and chemistry are often difficult subjects for quiz bowl teams if those classes are taught during the junior or senior years since many players will not have completed them before encountering the subject matter at tournaments. One high-yield area of physics to study is the nomenclature of various groups of particles.

Some conventions: The mass of particles is usually given in mega-electronvolts (MeV), where an electron-volt is the energy acquired by an electron when it crosses a potential difference of one volt. The energies are converted to masses by Einstein's famous equation E = mc², where c is the speed of light. Charges are given in terms of the fundamental electric charge (the absolute value of the charge on an electron).

Every kind of particle also has a corresponding anti-particle made of anti-matter; when it is said that there "six leptons," anti-particles are not counted (so, in some sense, there are twelve). Anti-particles have the same mass, but the opposite charge, of the original. There are no particles with negative mass. Note that in some rare situations, a particle can be its own anti-particle.

1. 
   Leptons are one of the classes of "fundamental particles" (meaning that they cannot be broken down into smaller particles). There are six "flavors" of leptons: the electron, the muon, the tauon, the electron neutrino (usually just called "the" neutrino), the muon neutrino, and the tauon neutrino. The three neutrinos are neutral (and were once thought to be massless), while the other three have a charge of -1. All neutrinos are fermions and the total number of leptons is conserved (counting regular leptons as +1 particle and anti-leptons as -1 particle). The word "lepton" comes from the Greek for "light" (as in "not heavy"), even though the muon and tauon are fairly massive.
   
2. 
   Quarks are another class of fundamental particle. They also come in six flavors: up, down, charm, strange, top (sometimes, "truth"), and bottom (sometimes, "beauty"). The up, charm, and top quarks have a charge of +2/3, while the down, strange, and bottom have a charge of -1/3. All quarks are fermions and they combine in pairs to form mesons and in triples to form baryons. The enormous mass of the top quark (178 GeV) made it difficult to create in particle accelerators, but its discovery in 1995 confirmed an essential element of the "Standard Model" of particle physics. The name "quark" comes from the line "Three quarks for Muster Mark" in Finnegans Wake that appealed to Murray Gell-Mann. The study of quarks (and the strong nuclear force) is quantum chromodynamics.
   
3. 
   Baryons are composite (i.e., non-fundamental) particles made from three quarks. The most common examples are the proton (two up quarks and one down quark) and the neutron (two down quarks and one up). All baryons are fermions. Quarks possess a characteristic called "color" (which has nothing to do with visual color) which can be either red, green, or blue (which are arbitrary names). A baryon must have one quark of each color so that the "total color" (analogous to mixing red, green, and blue light) is colorless (i.e., "white"). The word "baryon" comes from the Greek for "heavy." The total number of baryons is conserved (again, counting anti-baryons as -1).
   
4. 
   Mesons are composite particles generally made from a quark and an anti-quark. There are dozens of examples including the pion, kaon, J/Psi, Rho, and D. All mesons are bosons. The quark and anti-quark must have the same color (such as red and anti-red) so that the resulting meson is colorless (or "white"). It is also possible to make mesons out of two (or more) quarks and the same number of anti-quarks, but this kind of particle (a "tetraquark") is rare, both in nature and in quiz bowl.
   
5. 
   Fermions are particles with half-integral spin. Spin is a form of "intrinsic angular momentum" which is possessed by particles as if they were spinning around their axis (but, in fact, they aren't). The values cited for spin are not (usually) the real magnitude of that angular momentum, but the component of the angular momentum along one axis. Quantum mechanics restricts that component to being n/2 times Planck's constant divided by 2 pi for some integer n. If n is even, this results in "integral" spin, if it is odd, it results in "half-integral" spin. Note that the exact value of the spin itself is a real number; it's the multiplier of h/2pi that determines whether it is "integral" or not. The most significant thing about fermions is that they are subject to the Pauli Exclusion Principle: No two fermions can have the same quantum numbers (i.e., same state). The name "fermion" comes from that of the Italian-American physicist Enrico Fermi.
   
6. 
   Bosons are particles with integral spin. All particles are either bosons or fermions. The spin of a composite particle is determined by the total spin (i.e., the component of its intrinsic angular momentum along one axis) of its particles. For instance, an alpha particle (two protons and two neutrons) has four half-integral spin values. No matter how they are added up, the result will be an integral spin value (try it!), so an alpha particle is a (composite) boson. The Pauli Exclusion Principle does not apply to bosons (in fact, bosons prefer to be in the same quantum state). The name "boson" comes from that of the Indian-American physicist Satyendra Nath Bose.
   
7. 
   Hadrons are any particles made out of quarks (alternatively, any particle affected by the strong nuclear force). Generally, this means the baryons and the mesons. All hadrons are colorless (in the sense of the combined color of their constituent quarks). The name "hadron" comes from the Greek for "thick."
   
8. 
   Gauge bosons (sometimes called "vector bosons") are fundamental bosons that carry the forces of nature. That is, forces result from particles emitting and absorbing gauge bosons. The strong nuclear force is carried by gluons, the weak nuclear force is carried by the W, Z^-, and Z⁺ particles, the electromagnetic force is carried by the photon, and gravity is carried by the (as yet unobserved) graviton. The name comes from the role of "gauge theories" in describing the forces (which are beyond the scope of this article).
   
9. 
   Gluons are the gauge bosons that carry the strong nuclear force and bind hadrons together. Gluons have no charge and no mass, but do have color (in the sense of quarks). This color cannot be observed directly because the gluons are part of the larger hadron. The name comes from their role in "gluing" quarks together.
   
10. 
    Partons are an older name that was used for the "internal parts" of hadrons before the discovery and widespread acceptance of the quark model. Models based on partons are still used but, for the most part, it was determined that partons were quarks and the term is rarely used at the high school level except in historical contexts.
    

This You Gotta Know article is devoted to twelve computational areas that will help the most in solving the sorts of math questions that come up in NAQT invitational series. NAQT's collegiate sets tend to have very little computation and much of that is in the context of a specific field (physics, economics, chemistry, etc.).

1. 
   Pythagorean Triples. Almost certainly, the most important things to know are the basic sets of integers that satisfy the Pythagorean Theorem (a² + b² = c²) and could be the side lengths of a right triangle. These are called Pythagorean Triples and the simplest ones are 3-4-5, 5-12-13, 7-24-25, and 8-15-17. Note that any multiple of a Pythagorean Triple is also a Pythagorean Triple so that 6-8-10, 15-20-25, and 300-400-500 are also ones by virtue of 3-4-5 being one.
   
2. 
   Matrices. Every team should be able to add, subtract, multiply, take the determinant of, transpose, and invert matrices, particularly two-by-two ones.
   
3. 
   Vectors. Every team should be able to find the length of a vector, and add, subtract, find the angle between, the dot product of, and the cross product of two vectors.
   
4. 
   Solids. Teams should be able to calculate the volume and surface area of simple geometric figures including the sphere, cone, cylinder, pyramid, hemisphere, prism, and parallelepiped.
   
5. 
   Plane Figures. Teams should be able to calculate the areas of triangles (especially equilateral triangles), trapezoids, parallelograms, rhombi, and circles using different angles and lengths.
   
6. 
   Similar Figures. The areas of similar figures are related by the square of any corresponding length and the volumes are related by the cube of any corresponding length. For instance, if a square has a diagonal that is 30% longer than another square, it has an area that is (1.30 x 1.30 = ) 1.69 times as great (69% greater). Similar reasoning applies to perimeters, side lengths, diameters, and so forth.
   
7. 
   Permutations. Teams should be able to compute the number of permutations and combinations of n objects taken m at a time. They should also have memorized the first eight (or so) values of the factorial function to make this easier.
   
8. 
   Logarithms. Teams should be familiar with basic operations of logarithmic math: simplifying the logarithm of a product, difference, or power, and converting from one base to another.
   
9. 
   Complex Math. Teams should be familiar with the symbol i representing the imaginary square root of -1, basic operations on complex numbers, graphing complex numbers, and converting complex numbers to magnitude-angle form.
   
10. 
    Divisibility Rules. Teams should be able to quickly apply the divisibility rules for small integers (2 through 11) to large integers.
    
11. 
    Polynomial Math. Teams should be able to quickly add, subtract, multiply, divide, factor, and find the roots of low-degree polynomials.
    
12. 
    Calculus. Teams should be able to find the derivative, integral, slope-at-a-point, local extrema, and critical points of polynomial, trigonometric, and other common functions.
    

1. 
   C++ is a popular, compiled, high-level language developed by Bjarne Stroustrup in 1985 at Bell Labs. C++ is similar to C, but adds object-oriented features (classes), generic programming (templates), and exception handling to the language. It is a popular language for developing business applications and, increasingly, games.
   
2. 
   Java is a popular high-level language developed by Sun Microsystems in the early 1990s. The language was originally named OAK and unsuccessfully used for set-top devices, but hit it big after being renamed in 1995 and introduced to the World Wide Web. It is a relatively pure object-oriented language with syntax similar to C++. Instead of being compiled to object code, it is compiled to Java bytecode, which is then interpreted or compiled on the fly. This use of machine-independent bytecode gives it its "write once, run everywhere" property. Java is principally used for client-side web application ("applets") and server-side web application ("servlets") that make use of J2EE technology. The success of Java inspired Microsoft to introduce its C# language and .NET framework.
   
3. 
   BASIC (Beginner's All-purpose Symbolic Instruction Code) is a high-level language developed by John Kemeny and Thomas Kurtz at Dartmouth College in the mid 1960s. It is easy to use but its relative lack of structure makes maintaining programs difficult. There have been many versions of BASIC and some more modern ones (TurboBasic, QuickBasic Visual Basic) have added advanced features. Stereotypical programs like 10 PRINT "HELLO" and 10 GOTO 10 are written in BASIC.
   
4. 
   C, a compiled successor to the B programming language, was developed by Dennis Ritchie in 1972. It is a high-level and highly standardized language that remains very "close to the hardware" and allows the programmer to perform useful, fast, and dangerous tricks. It is widely used for business applications, games, operating systems (particularly UNIX and Linux), and device drivers.
   
5. 
   Perl is an interpreted language designed principally to process text. It was written by Larry Wall and first released in 1988. It is intended to be practical and concise rather than theoretically elegant and is sometimes lampooned as "write one, read never" because of its heavy use of symbols and idiom. It is often used for web CGI scripts and parsing log files. "Perl" is an unofficial retronym for "Practical Extraction Report Language."
   
6. 
   ALGOL (ALGOrithmic Language) was created in the late 1950s and was the first procedural language intended for solving mathematical and scientific problems. Formalized in a report titled ALGOL 58, it progressed through ALGOL 60 and ALGOL 68 before waning in popularity. ALGOL was sufficiently advanced and respected that most modern procedural languages reflect its overall structure and design; some, like Pascal, are very closely related.
   
7. 
   Pascal is a high-level, compiled language built upon ALGOL. It is named after the 17th-century mathematician Blaise Pascal and was developed by Niklaus Wirth during 1967-71. Pascal is best known for its emphasis on structured programming techniques and strong typing; because of this, it was extremely popular as a teaching language in the 1980s and early 1990s, though it was never popular for business or scientific applications. The object-oriented language Delphi was based on Pascal.
   
8. 
   LISP (LISt Processing) is the ancestor of the family of functional languages that emphasize evaluating expressions rather than executing imperative commands. It was developed in 1950-1960 by John McCarthy and is used primarily for symbolic manipulations of complicated structures rather than numerical calculation. It and its descendants (Scheme, CommonLisp, etc.) continue to be used in academic research, particularly artificial intelligence.
   
9. 
   Fortran (FORmula TRANslation) is the oldest high-level language. Designed by John Backus for IBM during the late 1950s, it was once in use on virtually every computer in the world and is still used today for engineering and scientific applications because of the quality of its compilers and numerical libraries. The most popular Fortran versions are Fortran IV, 77, and 90. The name "Fortran" was originally entirely capitalized, but the ANSI Fortran Committee has since declared the "initial capital" spelling official.
   
10. 
    COBOL (COmmon Business-Oriented Language) was developed in 1959 by CODASYL (Conference on Data Systems Languages) under the direction of Rear Admiral Grace Hopper and is the second-oldest high-level language. It emphasized record-processing and database access and uses an English-like syntax, all attributes that led to widespread use in business, particularly the financial sector. It is characterized as especially wordy (just as C and Perl are characterized as terse). The vast majority of Year 2000 problems involved programs written in COBOL.