Consider a triangle ABC in either hyperbolic or spherical geometryMathworldPlanetmath ( in which its angle sum in radians is Σ.

In hyperbolic geometry, the defect of ABC is δ(ABC)=π-Σ.

In spherical geometry, the defect of ABC is δ(ABC)=Σ-π.

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