Difference between revisions of "Excess of a triangle"
From Encyclopedia of Mathematics
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| − | The difference between the sum of the angles of a spherical triangle and two right angles. The excess | + | The difference between the sum of the angles of a spherical triangle and two right angles. The excess $\epsilon$ of a spherical triangle is proportional to its area $S$: $S=R^2\epsilon$, where $R$ is the radius of the sphere containing the spherical triangle. |
Latest revision as of 11:56, 5 July 2014
spherical excess, excess
The difference between the sum of the angles of a spherical triangle and two right angles. The excess $\epsilon$ of a spherical triangle is proportional to its area $S$: $S=R^2\epsilon$, where $R$ is the radius of the sphere containing the spherical triangle.
Comments
This notion is sometimes called the defect of the triangle (cf. Triangle, defect of a).
References
| [a1] | M. Berger, "Geometry" , II , Springer (1987) pp. 278 |
| [a2] | H.S.M. Coxeter, "Non-Euclidean geometry" , Univ. Toronto Press (1957) |
| [a3] | M. Greenberg, "Euclidean and non-Euclidean geometry" , Freeman (1980) pp. 105 |
How to Cite This Entry:
Excess of a triangle. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Excess_of_a_triangle&oldid=13640
Excess of a triangle. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Excess_of_a_triangle&oldid=13640
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article