Trigonometric constants expressed in real radicals in a regular polygon: a vertex, an edge center containing that vertex, and the polygon center. An "n"-gon can be divided into 2"n" right triangles with angles of , 90 − , 90} degrees, for "n" in 3, 4, 5, … Constructibility of 3, 4, 5, and 15-sided polygons are the basis, and angle bisectors allow multiples of two to also be derived. In degree format, sin and cos of 0, 30, 45, 60, and 90 can be calculated from their right angled triangles, using the Pythagorean theorem. In radian format, sin and cos of / 2 can be expressed
Sphere Many theorems from classical geometry hold true for spherical geometry as well, but not all do because the sphere fails to satisfy some of classical geometry's postulates, including the parallel postulate. In spherical trigonometry, angles are defined between great circles. Spherical trigonometry differs from ordinary trigonometry in many respects. For example, the sum of the interior angles of a spherical triangle always exceeds 180 degrees. Also, any two similar spherical triangles are congruent. In their book "Geometry and the Imagination" David Hilbert and Stephan Cohn-Vossen describe eleven properties of the sphere and discuss whether these properties uniquely determine the sphere.