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Triangles on a Sphere

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This Demonstration shows a spherical triangle. Three 2D sliders on the left control the vertices with spherical coordinates and sliding horizontally from 0 to 360° and vertically from 0 to 180°, respectively.

Contributed by: Borut Levart (March 2011)
Open content licensed under CC BY-NC-SA

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Geometry on a sphere is a noneuclidean geometry. Straight lines are represented as great circles and edges of a spherical triangle are parts of these great circles. The sum of the angles of a spherical triangle is always greater than 180°.

Snapshot 1: vertices close together form a triangle with the sum of its angles close to 180°

Snapshot 2: a triangle with three right angles, with angle a sum equal to 270°

Snapshot 3: all vertices lying on one great circle give an angle sum of 540°

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