Geometry, Spherical Geometry

Spherical Geometry deals with the geometry on the two-dimensional surface of a sphere. It explores concepts like great circles, spherical triangles (whose angles sum to more than 180 degrees), and shortest paths between points on a sphere. Questions involve properties of shapes on a sphere.

• Question

  In space, there are 30 non-degenerate vectors. Prove that there are at least 2 such that the angle between them is no greater than 45 degrees. 
  A. Tulpigo

  Topics:

  Geometry -> Trigonometry Geometry -> Spherical Geometry Combinatorics -> Pigeonhole Principle Combinatorics -> Combinatorial Geometry Geometry -> Plane Geometry -> Angle Calculation Geometry -> Vectors
  Sources:
  • Tournament of Towns, 1979-1980, Main, Spring Question 4