defect

Consider a triangle $\triangle ABC$ in either hyperbolic or spherical geometry 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 triangle is equal to its defect.