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Hyperbolic Triangle

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HyperbolicTriangle

A hyperbolic triangle is a region in the hyperbolic plane bounded by three geodesic segments. If its angles are A, B, and C, then A+B+C<pi. For curvature -R^(-2), its area is

A=R^2(pi-A-B-C).

Thus the angular defect determines the area. Relations among the side lengths and angles are given by the hyperbolic law of cosines, hyperbolic law of sines, and hyperbolic law of tangents (Anderson 1999).

See also

Area, Geodesic, Hyperbolic Geometry, Hyperbolic Law of Cosines, Hyperbolic Law of Sines, Hyperbolic Law of Tangents, Hyperbolic Plane, Spherical Triangle, Triangle

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References

Anderson, J. W. Hyperbolic Geometry. New York: Springer-Verlag, 1999.

Cite this as:

Weisstein, Eric W. "Hyperbolic Triangle." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/HyperbolicTriangle.html

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