Spherical Triangle
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A spherical triangle is a figure formed on the surface of a sphere by three great circular arcs intersecting pairwise in threevertices. The spherical triangle is the spherical analog of the planar Triangle. Let a spherical triangle haveAngles 
, 
, and 
and Radius 
. Then the Area of the spherical triangle is
The sum of the angles of a spherical triangle is between
and 
radians (180° and 540°). Theamount by which it exceeds 180° is called the Spherical Excess and is denoted 
or 
.The study of angles and distances of figures on a sphere is known as Spherical Trigonometry.
See also Colunar Triangle, Girard's Spherical Excess Formula, L'Huilier's Theorem, Spherical Polygon,Spherical Trigonometry
References
Abramowitz, M. and Stegun, C. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 79, 1972.
Beyer, W. H. CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, pp. 131 and 147-150, 1987.
- Rhombitruncated Icosidodecahedron
- Rhombohedron
- Rhomboid
- Rhomboidal Dodecahedron
- Rhombus
- Rhumb Line
- Ribbon Knot
- Ribet's Theorem
- Riccati-Bessel Functions
- Riccati Differential Equation
- Ricci Curvature
- Ricci Tensor
- Rice Distribution
- Richardson Extrapolation
- Richardson's Theorem
- Richard's Paradox
- Ridders' Method
- Ridge
- Riemann-Christoffel Tensor
- Riemann Curve Theorem
- Riemann Differential Equation
- Riemann Function
- Riemann Hypothesis
- Riemannian Geometry
- Riemannian Geometry (Non-Euclidean)