# defect

Consider a triangle $\triangle ABC$ in either hyperbolic or spherical geometry (http://planetmath.org/NonEuclideanGeometry) in which its angle sum in radians is $\Sigma$.

In hyperbolic geometry, the defect of $\triangle ABC$ is $\delta(\triangle ABC)=\pi-\Sigma$.

In spherical geometry, the defect of $\triangle ABC$ is $\delta(\triangle ABC)=\Sigma-\pi$.

Note that, in both hyperbolic and spherical geometry, the area of a is equal to its defect.

Title defect Defect 2013-03-22 16:05:22 2013-03-22 16:05:22 Wkbj79 (1863) Wkbj79 (1863) 10 Wkbj79 (1863) Definition msc 51M10 msc 51-00 AreaOfASphericalTriangle