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: 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: He incorporated Eastern ideas, free-jazz tendencies and boundless energy in such pieces as My Favorite Things, Sun Ship and Meditations. His first jazz recordings were with Dizzy Gillespie's band; he joined the original Miles Davis Quintet in 1955, but was booted because of heroin addiction two years later. He then quit heroin, had a religious awakening and rejoined Miles Davis in early 1958. He would leave, however, to form his own quartet. For 10 points-name this tenor saxophonist whose masterwork was 1964's A Love Supreme.

SOLUTION: Fine Arts

PROBLEM: One player of this instrument composed songs such as "Billie's Bounce" and "Now's the Time. "" Another player of it included the songs "Countdown" and "Naima" on his album Giant Steps. Those players of this instrument made the albums Ornithology and A Love Supreme and are Charlie "Bird" Parker and John Coltrane. For 20 points, name this family of instruments important in jazz, a single-reed wind instrument made of brass and named for its inventor Adolph.

SOLUTION:
Fine Arts