mgor/protobowl-11-13 huggingface dataset:
Category: Science
Question: One method of performing this action involves using a base case and an induction step; another method begins by assuming the opposite and finding something impossible, which is the type "by contradiction". In 1994 Andrew Wiles did this for (*) Fermat's [fair-mah'z] Last Theorem. Basic geometry often uses the "two-column" variety of, for 10 points, what process of showing that a mathematical statement is true?
Answer: mathematical {proof} [accept word forms]

A mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The argument may use other previously established statements, such as theorems; but every proof can, in principle, be constructed using only certain basic or original assumptions known as axioms, along with the accepted rules of inference. Proofs are examples of exhaustive deductive reasoning which establish logical certainty, to be distinguished from empirical arguments or non-exhaustive inductive reasoning which establish "reasonable expectation". Presenting many cases in which the statement holds is not enough for a proof, which must demonstrate that the statement is true in all possible cases. A proposition that has not been proved but is believed to be true is known as a conjecture, or a hypothesis if frequently used as an assumption for further mathematical work.
Proofs employ logic expressed in mathematical symbols, along with natural language which usually admits some ambiguity. In most mathematical literature, proofs are written in terms of rigorous informal logic. Purely formal proofs, written fully in symbolic language without the involvement of natural language, are considered in proof theory. The distinction between formal and informal proofs has led to much examination of current and historical mathematical practice, quasi-empiricism in mathematics, and so-called folk mathematics, oral traditions in the mainstream mathematical community or in other cultures. The philosophy of mathematics is concerned with the role of language and logic in proofs, and mathematics as a language.
Category: Science
Question: This type of respiration takes place when limited oxygen is available. It is used to make sauerkraut, kimchi, and yogurt, and can be carried out by (*) microorganisms such as yeast. For 10 points, name this process in which sugars are converted into ethanol, examples of which include the conversion of grapes to wine and wheat to beer.
Answer: {fermentation} [accept word forms; prompt on {\"anaerobic\" respiration}]

Fermentation is a metabolic process that produces chemical changes in organic substances through the action of enzymes. In biochemistry, fermentation is narrowly defined as the extraction of energy from carbohydrates in the absence of oxygen, while in food production, it may more broadly refer to any process in which the activity of microorganisms brings about a desirable change to a foodstuff or beverage. The science of fermentation is known as zymology.
In microorganisms, fermentation is the primary means of producing adenosine triphosphate (ATP) by the degradation of organic nutrients anaerobically.
Humans have used fermentation to produce foodstuffs and beverages since the Neolithic age. For example, fermentation is used for preservation in a process that produces lactic acid found in such sour foods as pickled cucumbers, kombucha, kimchi, and yogurt, as well as for producing alcoholic beverages such as wine and beer. See Fermentation in food processing. Fermentation also occurs within the gastrointestinal tracts of all animals, including humans.
Industrial fermentation is a broader term used for the process of applying microbes for the large-scale production of chemicals, biofuels, enzymes, proteins and pharmaceuticals.
Category: Fine Arts
Question: In one opera by this man, the soldiers Ferrando and Guglielmo (“gool-YELL-mo”) test their wives by seducing them in the guise of Albanians. This man also wrote an opera in which the title seducer is dragged to hell by the statue of Il Commendatore (“EEL co-MEN-dah-TORR-ee”). For 10 points, name this Austrian composer of the operas Cosi Fan Tutte (“CO-see fan TOO-tee”) and Don Giovanni as well as A Little Night Music, who allegedly feuded with Salieri.
Answer: Wolfgang Amadeus {Mozart}

Wolfgang Amadeus Mozart (27 January 1756 – 5 December 1791) was a prolific and influential composer of the Classical period. Despite his short life, his rapid pace of composition resulted in more than 800 works representing virtually every Western classical genre of his time. Many of these compositions are acknowledged as pinnacles of the symphonic, concertante, chamber, operatic, and choral repertoire. Mozart is widely regarded as one of the greatest composers in the history of Western music, with his music admired for its "melodic beauty, its formal elegance and its richness of harmony and texture".
Born in Salzburg, then in the Holy Roman Empire and currently in Austria, Mozart showed prodigious ability from his earliest childhood. At age five he was already competent on keyboard and violin, he had begun to compose, and he performed before European royalty. His father took him on a grand tour of Europe and then three trips to Italy. At 17, he was a musician at the Salzburg court but grew restless and travelled in search of a better position. Mozart’s search for employment led to positions in Paris, Mannheim, Munich, and again in Salzburg, during which he wrote his five violin concertos,  Sinfonia Concertante, and Concerto for Flute and Harp, as well as sacred pieces and masses, the motet Exsultate Jubilate, and the opera Idomeneo, among other works. 
While visiting Vienna in 1781, Mozart was dismissed from his Salzburg position. He stayed in Vienna, where he achieved fame but little financial security. During Mozart’s early years in Vienna, he  produced several notable works, such as the opera Die Entführung aus dem Serail, the Great Mass in C Minor, the "Haydn" Quartets and a number of symphonies. Throughout his Vienna years, Mozart composed over a dozen piano concertos, many considered some of his greatest achievements. In the final years of his life, Mozart wrote many of his best-known works, including his last three symphonies, culminating in the Jupiter Symphony, the serenade Eine kleine Nachtmusik, his Clarinet Concerto, the four operas Le Nozze di Figaro, Don Giovanni, Così fan tutte and The Magic Flute and his Requiem. The Requiem was largely unfinished at the time of his death at age 35, the circumstances of which are uncertain and much mythologised.
Category: Science
Question: This unit has gram and kilogram types depending on the amount of water used to define it. Its name is based on the Latin word for "heat". The gram type is a little over four joules, a unit that has in many contexts become a more common unit of (*) energy than this one. For 10 points, name this unit whose kilogram type is also known as the dietary type and is still used to measure the energy content of food.
Answer: calorie

The calorie is a unit of energy that originated from the caloric theory of heat. The large calorie, food calorie, dietary calorie, or kilogram calorie is defined as the amount of heat needed to raise the temperature of one liter of water by one degree Celsius (or one kelvin). The small calorie or gram calorie is defined as the amount of heat needed to cause the same increase in one milliliter of water. Thus, 1 large calorie is equal to 1000 small calories. 
In nutrition and food science, the term calorie and the symbol cal may refer to the large unit or to the small unit in different regions of the world. It is generally used in publications and package labels to express the energy value of foods in per serving or per weight, recommended dietary caloric intake, metabolic rates, etc. Some authors recommend the spelling Calorie and the symbol Cal (both with a capital C) if the large calorie is meant, to avoid confusion; however, this convention is often ignored.
In physics and chemistry, the word calorie and its symbol usually refer to the small unit, the large one being called kilocalorie (kcal). However, the kcal is not officially part of the International System of Units (SI), and is regarded as obsolete, having been replaced in many uses by the SI derived unit of energy, the joule (J), or the kilojoule (kJ) for 1000 joules.
The precise equivalence between calories and joules has varied over the years, but in thermochemistry and nutrition it is now generally assumed that one (small) calorie (thermochemical calorie) is equal to exactly 4.184 J, and therefore one kilocalorie (one large calorie) is 4184 J or 4.184 kJ.
Category: Science
Question: This compound is converted to Vitamin D in the presence of ultraviolet-B light. It is carried in the blood by lipoproteins (“LIPE-oh-PRO-teens”), with the “good” kind carried by high-density ones. The “bad” kind, carried by LDLs, can build up on arteries to form plaques. For 10 points, 300 milligrams per day is the recommended dietary allowance of what waxy substance, high levels of which place an individual at greater risk for heart disease?
Answer: {cholesterol}

Cholesterol is the principal sterol of all higher animals, distributed in body tissues, especially the brain and spinal cord, and in animal fats and oils.
Cholesterol is biosynthesized by all animal cells and is an essential structural component of animal cell membranes. In vertebrates, hepatic cells typically produce the greatest amounts. In the brain, astrocytes produce cholesterol and transport it to neurons. It is absent among prokaryotes (bacteria and archaea), although there are some exceptions, such as Mycoplasma, which require cholesterol for growth. Cholesterol also serves as a precursor for the biosynthesis of steroid hormones, bile acid and vitamin D.
Elevated levels of cholesterol in the blood, especially when bound to low-density lipoprotein (LDL, often referred to as "bad cholesterol"), may increase the risk of cardiovascular disease.
François Poulletier de la Salle first identified cholesterol in solid form in gallstones in 1769. In 1815, chemist Michel Eugène Chevreul named the compound "cholesterine".
Category: Religion
Question: Before he was born, his parents learned that he was not to touch a dead body, and he was to abstain from strong drink. He was involved with a Timnite woman and a harlot before meeting the woman that would betray him. He died during the collapse of a temple to Dagon (“DAY-gon”), but by destroying it, he got his revenge on the Philistines. For 10 points, name this lover of Delilah who lost his power after his hair was cut.
Answer: {Samson}

Samson (; Hebrew: שִׁמְשׁוֹן Šīmšōn "man of the sun") was the last of the judges of the ancient Israelites mentioned in the Book of Judges (chapters 13 to 16) and one of the last leaders who "judged" Israel before the institution of the monarchy. He is sometimes considered as an Israelite version of the popular Near Eastern folk hero also embodied by the Sumerian Gilgamesh and Enkidu, as well as the Greek Heracles. Samson was given superhuman powers by God in the form of extreme strength.
The biblical account states that Samson was a Nazirite and that he was given immense strength to aid him against his enemies and allow him to perform superhuman feats, including slaying a lion with his bare hands and massacring a Philistine army with a donkey's jawbone after offending groomsmen at his wedding to one. The cutting of Samson's long hair would violate his Nazirite vow and nullify his ability.
Samson is betrayed by his lover Delilah, who, sent by Philistine officials to entice him, orders a servant to cut his hair while he is sleeping and turns him over to the Philistines, who gouge out his eyes and force him to mill grain at Gaza City. While there, his hair begins to grow again. When the Philistines take Samson into their temple of Dagon, Samson asks to rest against one of the support pillars. After being granted permission, he prays to God and miraculously recovers his strength, allowing him to bring down the columns – collapsing the temple and killing both himself and the Philistines. In some Jewish traditions, Samson is believed to have been buried in Zorah in Israel overlooking the Sorek valley (also considered his birthplace). 
Samson has been the subject of rabbinic, Christian, and Islamic commentary, with some Christians viewing him as a type of Jesus, based on similarities between their lives. Notable depictions of Samson include John Milton's closet drama Samson Agonistes and Cecil B. DeMille's 1949 Hollywood film Samson and Delilah. Samson also plays a major role in Western art and traditions.
Category: Science
Question: The uniform probability distribution takes this shape. Rotating this shape using one of its sides as an axis yields a cylinder. This shape is traced out by the x-axis, the y-axis, and the equations x equals two and y equals six. Each diagonal of this kind of quadrilateral divides it into two congruent right triangles. For 10 points, give this shape that has four right angles.
Answer: {rectangles} [do not accept or prompt on "square"]

In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°); or a parallelogram containing a right angle. A rectangle with four sides of equal length is a square. The term "oblong" is used to refer to a non-square rectangle. A rectangle with vertices ABCD would be denoted as  ABCD.
The word rectangle comes from the Latin rectangulus, which is a combination of rectus (as an adjective, right, proper) and angulus (angle).
A crossed rectangle is a crossed (self-intersecting) quadrilateral which consists of two opposite sides of a rectangle along with the two diagonals (therefore only two sides are parallel). It is a special case of an antiparallelogram, and its angles are not right angles and not all equal, though opposite angles are equal. Other geometries, such as spherical, elliptic, and hyperbolic, have so-called rectangles with opposite sides equal in length and equal angles that are not right angles.
Rectangles are involved in many tiling problems, such as tiling the plane by rectangles or tiling a rectangle by polygons.
Category: Religion
Question: Ancient practitioners of this art form include Polykleitos (PAHL-ee-KLY-tohss), whose Doryphoros (dorr-ee-FOR-ohss) is one of the oldest Greek works that still exists. Other practitioners of this art form include Phidias and Myron. Modern works of this type include Frederic Remington's Bronco Buster. For 10 points, name this type of art exemplified by Michelangelo's Pieta and The Thinker by Auguste Rodin.
Answer: sculpture [or word forms, such as sculpting]

Sculpture is the branch of the visual arts that operates in three dimensions. Sculpture is the three-dimensional art work which is physically presented in the dimensions of height, width and depth. It is one of the plastic arts. Durable sculptural processes originally used carving (the removal of material) and modelling (the addition of material, as clay), in stone, metal, ceramics, wood and other materials but, since Modernism, there has been almost complete freedom of materials and process. A wide variety of materials may be worked by removal such as carving, assembled by welding or modelling, or moulded or cast.
Sculpture in stone survives far better than works of art in perishable materials, and often represents the majority of the surviving works (other than pottery) from ancient cultures, though conversely traditions of sculpture in wood may have vanished almost entirely. However, most ancient sculpture was brightly painted, and this has been lost.
Sculpture has been central in religious devotion in many cultures, and until recent centuries, large sculptures, too expensive for private individuals to create, were usually an expression of religion or politics. Those cultures whose sculptures have survived in quantities include the cultures of the ancient Mediterranean, India and China, as well as many in Central and South America and Africa.
The Western tradition of sculpture began in ancient Greece, and Greece is widely seen as producing great masterpieces in the classical period. During the Middle Ages, Gothic sculpture represented the agonies and passions of the Christian faith. The revival of classical models in the Renaissance produced famous sculptures such as Michelangelo's statue of David. Modernist sculpture moved away from traditional processes and the emphasis on the depiction of the human body, with the making of constructed sculpture, and the presentation of found objects as finished artworks.
Category: Science
Question: These phenomena are counted using the Wolf number, and butterfly diagrams show the concentration of these regions in latitude bands. Coronal loops and mass ejections generally originate from these regions. Though they are not eclipses, they possess an umbra and penumbra. These electromagnetic phenomena go through a variation cycle of about (*) 11 years. For 10 points, name these cooler areas on the Sun's photosphere that appear dark.
Answer: {sunspots}

Sunspots are temporary spots on the Sun's surface that are darker than the surrounding area. They are regions of reduced surface temperature caused by concentrations of magnetic flux that inhibit convection. Sunspots appear within active regions, usually in pairs of opposite magnetic polarity. Their number varies according to the approximately 11-year solar cycle.
Individual sunspots or groups of sunspots may last anywhere from a few days to a few months, but eventually decay. Sunspots expand and contract as they move across the surface of the Sun, with diameters ranging from 16 km (10 mi) to 160,000 km (100,000 mi). Larger sunspots can be visible from Earth without the aid of a telescope. They may travel at relative speeds, or proper motions, of a few hundred meters per second when they first emerge.
Indicating intense magnetic activity, sunspots accompany other active region phenomena such as coronal loops, prominences, and reconnection events. Most solar flares and coronal mass ejections originate in these magnetically active regions around visible sunspot groupings. Similar phenomena indirectly observed on stars other than the Sun are commonly called starspots, and both light and dark spots have been measured.
Category: Science
Question: The NASA Juno spacecraft is destined for this body in 2016, when it will observe this body's magnetic field and determine the ratio of hydrogen to oxygen in its atmosphere. Its closest Galilean satellite is partially molten because of tidal forces, and is called Io. This planet contains cyclones called the Little and (*) Great Red Spots. For 10 points, name this gas giant, the largest planet in the solar system.
Answer: Jupiter

Jupiter is the fifth planet from the Sun and the largest in the Solar System. A gas giant, Jupiter's mass is more than two and a half times that of all the other planets in the Solar System combined and slightly less than one one-thousandth the mass of the Sun. Jupiter orbits the Sun at a distance of 5.20 AU (778.5 Gm) with an orbital period of 11.86 years. It is the third brightest natural object in the Earth's night sky after the Moon and Venus and has been observed since prehistoric times. Its name derives from Jupiter, the chief deity of ancient Roman religion.
Jupiter was the first planet to form, and its inward migration during the primordial Solar System impacted much of the formation history of the other planets. Hydrogen constitutes 90% of Jupiter's volume, followed by helium, which forms 25% of its mass and 10% of its volume. The ongoing contraction of Jupiter's interior generates more heat than the planet receives from the Sun. Its internal structure is believed to consist of an outer mantle of fluid metallic hydrogen and a diffuse inner core of denser material. Because of its rapid rotation rate of one rotation per ten hours, Jupiter's shape is an oblate spheroid; it possesses a slight but noticeable bulge around the equator. The outer atmosphere is divided into a series of latitudinal bands, with turbulence and storms along their interacting boundaries. The most obvious result of this is the Great Red Spot, a giant storm that has been recorded since at least 1831.
Jupiter is surrounded by a faint planetary ring system and has a powerful magnetosphere, the second largest contiguous structure in the Solar System (after the heliosphere). Jupiter forms a system of 95 known moons and probably many more, including the four large moons discovered by Galileo Galilei in 1610: Io, Europa, Ganymede, and Callisto. Ganymede, the largest of the four, is larger than the planet Mercury. Callisto is the second largest; Io and Europa are approximately the size of Earth's Moon.
Since 1973, Jupiter has been visited by nine robotic probes: seven flybys and two dedicated orbiters, with one more en route and one awaiting launch.
Category: Religion
Question: This person was described as a "beloved physician" by a "coworker," and this man's feast day is October 18. He dedicated two books to Theophilus (thee-AH-fill-uss), including one that begins with the Ascension and describes the missionary journeys of that "coworker," Paul. For 10 points, name this author of Acts of the Apostles and the third Gospel of the New Testament.
Answer: St. Luke

Luke the Evangelist is one of the Four Evangelists—the four traditionally ascribed authors of the canonical gospels. The Early Church Fathers ascribed to him authorship of both the Gospel of Luke and the Acts of the Apostles. Prominent figures in early Christianity such as Jerome and Eusebius later reaffirmed his authorship, although a lack of conclusive evidence as to the identity of the author of the works has led to discussion in scholarly circles, both secular and religious.
The New Testament mentions Luke briefly a few times, and the Epistle to the Colossians refers to him as a physician (from Greek for 'one who heals'); thus he is thought to have been both a physician and a disciple of Paul.
Since the early years of the faith, Christians have regarded him as a saint. He is believed to have been a martyr, reportedly having been hanged from an olive tree, though some believe otherwise. The Catholic Church and other major denominations venerate him as Saint Luke the Evangelist and as a patron saint of artists, physicians, bachelors, notaries, butchers, brewers, and others; his feast day is 18 October.