Question

Thurston proved that a knot must have this property if it is not a torus knot or a satellite knot. A space with this property has as its orientation-preserving isometries the group of real Möbius transformations with determinant one. Spaces with this property have curves called horocycles, can be modeled in two dimensions by Poincaré’s half-plane and disk, and have constant negative curvature. This property is the first word in a class of functions derived from the pair “e-to-the-x plus-or-minus e-to-the-negative-x all over two.” Lobachevsky (10[1])names a non-Euclidean geometry (10[1])with this property, which breaks the parallel postulate and has triangles whose angles sum to less than 180 degrees. For 10 points, what property derives from the name of a conic section exemplified by the function one-over-x? ■END■ (10[1])

ANSWER: hyperbolic [accept hyperbola; accept hyperbolic functions or hyperbolic trigonometric functions]
<Oxford A, Other Science>
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Buzzes

PlayerTeamOpponentBuzz PositionValue
Bill ZhaoFlorida BUCF C8410
Leo LawFlorida AValencia A8810
Juan LandaetaFlorida State AUCF B12610

Summary

Florida2025-02-01Y3100%0%0%99.33
Great Lakes2025-02-01Y6100%0%17%85.50
Lower Mid-Atlantic2025-02-01Y683%0%0%88.00
Midwest2025-02-01Y6100%0%0%90.50
North2025-02-01Y3100%0%0%76.67
Northeast2025-02-01Y5100%0%0%73.40
Overflow2025-02-01Y475%0%50%111.67
Pacific Northwest2025-02-01Y2100%0%0%79.50
South Central2025-02-01Y2100%0%0%80.50
Southeast2025-02-01Y4100%0%0%99.50
Upper Mid-Atlantic2025-02-01Y9100%0%0%78.56
Upstate NY2025-02-01Y3100%0%0%90.33