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.

Title	defect
Canonical name	Defect
Date of creation	2013-03-22 16:05:22
Last modified on	2013-03-22 16:05:22
Owner	Wkbj79 (1863)
Last modified by	Wkbj79 (1863)
Numerical id	10
Author	Wkbj79 (1863)
Entry type	Definition
Classification	msc 51M10
Classification	msc 51-00
Related topic	AreaOfASphericalTriangle