derivation of surface area measure on sphere

The sphere of radius r can be described parametrically by spherical coordinatesMathworldPlanetmath (what else ;) ) as follows:


Then, using trigonometric identities to simplify expressions we find that


and hence, using more trigonometric identities, we find that


This means that, on a sphere


Note that in the case of a unit sphereMathworldPlanetmath, (r=1) this agrees with the formula presented in the second paragraph of subsection 2 of the main entry.

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Title derivation of surface area measure on sphere
Canonical name DerivationOfSurfaceAreaMeasureOnSphere
Date of creation 2013-03-22 14:57:55
Last modified on 2013-03-22 14:57:55
Owner rspuzio (6075)
Last modified by rspuzio (6075)
Numerical id 6
Author rspuzio (6075)
Entry type Derivation
Classification msc 28A75