Excess of a triangle

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