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Area Element

The area element for a surface with first fundamental form

ds^2=Edu^2+2Fdudv+Gdv^2

is

dA=sqrt(EG-F^2)du ^ dv,

where du ^ dv is the wedge product.

See also

Area, First Fundamental Form, Line Element, Riemannian Metric, Surface Area, Volume Element

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References

Gray, A. "The Intuitive Idea of Area on a Surface." §15.3 in Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press, pp. 351-353, 1997.

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Area Element

Cite this as:

Weisstein, Eric W. "Area Element." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/AreaElement.html

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