spherical triangle
Quick Summary
A spherical triangle is a polygon with three sides formed by the intersection of three great circle arcs on the surface of a sphere. This area of mathematics, known as spherical trigonometry, was studied extensively in antiquity for its applications in navigation, cartography, and astronomy.12
Unlike planar triangles, the sum of the angles in a spherical triangle is always greater than 180 degrees. The excess over 180 degrees is called the spherical excess, and it is directly related to the area of the triangle. Formulas analogous to those in plane trigonometry, such as the law of sines and the law of cosines, exist for spherical triangles.23
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- Menelaus of Alexandria
…first conceived and defined a spherical triangle (a triangle formed by three arcs of great circles on the surface of a sphere).
Read More…first conceived and defined a spherical triangle (a triangle formed by three arcs of great circles on the surface of a sphere).
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trigonometryPassage to EuropeThe first definition of a spherical triangle is contained in Book 1 of the Sphaerica, a three-book treatise by Menelaus of Alexandria (c. 100 ce) in which Menelaus developed the spherical equivalents of Euclid’s propositions for planar triangles. A spherical triangle was understood to mean a figure formed on the…
Read MoreThe first definition of a spherical triangle is contained in Book 1 of the Sphaerica, a three-book treatise by Menelaus of Alexandria (c. 100 ce) in which Menelaus developed the spherical equivalents of Euclid’s propositions for planar triangles. A spherical triangle was understood to mean a figure formed on the…
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