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.

Ex Input:
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.

Ex Output:
Science


Ex Input:
The Hilbert Basis Theorem guarantees that if one of these is Noetherian, then the polynomials over it are also Noetherian. While the existence of a multiplicative unit in one of these isnt guaranteed by the axioms, most authors assume its presence. These can form quotients with special subsets known as ideals, and commutative ones with no zero divisors are known as integral domains. Formally an abelian group over addition and a monoid over multiplication, this describes, for ten points, what algebraic structure exemplified by the integers

Ex Output:
Science


Ex Input:
In quantum mechanical systems, this can be defined as the negative trace of the density matrix multiplied by the log of the density matrix. For a gas of photons, this quantity is directly proportional to the total number of photons. Pressure can be calculated as temperature times the partial derivative of this quantity with respect to volume. The Sackur-Tetrode equation gives the value of this for an ideal gas, while inverse temperature is equal to the derivative of this with respect to energy. It is generally defined as Boltzmann's constant times the logarithm of the number of microstates. FTP, identify this quantity that always increases according to the 2nd Law of Thermodynamics.

Ex Output:

Science


