TASK DEFINITION: In this task you will be given a text passage from a trivia quiz. You should choose the category this question belongs to from these categories: History, Science, Social Science, Fine Arts, Literature. You can only choose one category, so if in doubt, please choose the closest match.
PROBLEM: Melamine resin is formed by dehydration of this compound, while barbiturates can also be formed by addition of this compound to malonic acid. Other uses of this compound include separation of racemic mixtures. Originally produced by a reaction between silver cyanate with ammonium chloride, it is now made in indusrial quantities by heating carbon dioxide with ammonia. When arginine is split, it forms an ornithine molecule and a molecule of this; the principal end product of mammalian nitrogen metabolism. First isolated by H.M. Rouelle, FTP, name the compound used to disprove the theory of vitalism when, in 1828 Friedrich Wohler, first synthesized it from inorganic materials.

SOLUTION: Science

PROBLEM: Loewner's inequality relates the area and systole of Riemannian metrics on one of these spaces. Arnold's cat map is a chaotic mapping from one of these spaces to itself. This name is given to connected, compact, abelian Lie subgroups, and any compact Lie group has a maximal one. Dupin cyclides are geometric inversions of these objects, and two Villarceau circles can be created by cutting one of these objects diagonally. N-dimensional versions of these objects, which have genus one, are homeomorphic to the Cartesian product of N circles. Other than the Klein bottle, these are the only closed, compact surfaces with an Euler characteristic of zero. They can be created by revolving a circle around an axis coplanar to the circle's diameter. For 10 points, name these mathematical objects that often look like doughnuts.

SOLUTION: Science

PROBLEM: Juan de Urtubia led the sacking of this city by the Navarrese Company 68 years after it was captured by the Catalan Company following the battle of Halmyros. It is generally assumed that this city gained control of two additional districts in a confederacy following its 427 BCE capture of Plataea. Cassander repaired the damage this city suffered following its unsuccessful revolt against the League of Corinth, which came 3 years after its defeat alongside Athens at Chaeronea. Philip II of Macedon spent time as a captive in this city, giving him an opportunity to study the improved phalanx tactics developed by Epaminondas. FTP name this polis which enjoyed a few decades of hegemony on the strength of its Sacred Band.

SOLUTION:
History