A mathematical subject dealing with the numerical relationships among the sides and the angles of a triangle. In plane trigonometry the triangle to be studied is formed by selecting three points in a two-dimensional plane (so that all three points do not lie on the same straight line) and connecting each pair of points with a straight line segment. In spherical trigonometry the triangle to be studied is formed by selecting three points on the two-dimensional surface of a three-dimensional sphere (so that all three points do not lie on the same great circle) and connecting each pair of points with an arc of the great circle that they determine on the sphere.

Excerpt from the Encyclopedia Britannica without permission.