# Four Theorems on Spherical Triangles

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Draw a spherical triangle on the surface of a unit sphere centered at . Let the sides opposite the corresponding vertices be the arcs , , . Let , , be the angles at the vertices , , ; , , are also the dihedral angles of a trihedron with apex and edges , , . Let , , be the angles of at . Let , , be points on the sides (or their extensions) opposite to , , . Define the unit vectors , , .

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Contributed by: Izidor Hafner (March 2017)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

This Demonstration is based on problem 5.34 in [3, p. 88].

References

[1] Wikipedia. "Spherical Law of Cosines." (Mar 15, 17) en.wikipedia.org/wiki/Spherical_law_of _cosines.

[2] Wikipedia. "Spherical Trigonometry." (Mar 15, 2017) en.wikipedia.org/wiki/Spherical_trigonometry.

[3] V. V. Prasolov and I. F. Sharygin, *Problems in Stereometry* (in Russian), Moscow: Nauka, 1989.

[4] Wikipedia. "Ceva's Theorem." (Mar 15, 2017) en.wikipedia.org/wiki/Ceva%27 s_theorem.

## Permanent Citation

"Four Theorems on Spherical Triangles"

http://demonstrations.wolfram.com/FourTheoremsOnSphericalTriangles/

Wolfram Demonstrations Project

Published: March 16 2017