View source for Excess of a triangle

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''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|Triangle, defect of a]]).

====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  M. Berger,   "Geometry" , '''II''' , Springer  (1987)  pp. 278</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top">  H.S.M. Coxeter,   "Non-Euclidean geometry" , Univ. Toronto Press  (1957)</TD></TR><TR><TD valign="top">[a3]</TD> <TD valign="top">  M. Greenberg,   "Euclidean and non-Euclidean geometry" , Freeman  (1980)  pp. 105</TD></TR></table>