defect

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

In hyperbolic geometry, the defect of $\mathrm{△}ABC$ is $\delta (\mathrm{△}ABC)=\pi -\mathrm{\Sigma }$.

In spherical geometry, the defect of $\mathrm{△}ABC$ is $\delta (\mathrm{△}ABC)=\mathrm{\Sigma }-\pi$.

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