© Blayne Heckel.

Shapes with corners appear different depending on the curvature of space. In flat space, the sum of the angles in a triangle is 180 degrees. For a positively curved space, such as the surface of a sphere, the sum of the interior angles of a triangle exceeds 180 degrees. For a negatively curved space, such as a saddle, the angles of a triangle sum to less than 180 degrees. (Unit: 3)