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Homedefect

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# 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.

Related:

AreaOfASphericalTriangle

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

51M10*no label found*51-00

*no label found*

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