PlanetMath: defect

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defect

(Definition)

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.

"defect" is owned by Wkbj79.

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Cross-references: area, spherical geometry, hyperbolic geometry, radians, angle sum, triangle
There are 5 references to this entry.

This is version 7 of defect, born on 2006-07-19, modified 2007-06-26.
Object id is 8150, canonical name is Defect.
Accessed 1697 times total.

Classification:

AMS MSC:	51-00 (Geometry :: General reference works )
	51M10 (Geometry :: Real and complex geometry :: Hyperbolic and elliptic geometries and generalizations)

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