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Line Element

Also known as the first fundamental form,

ds^2=g_(ab)dx^adx^b.

In the principal axis frame for three dimensions,

ds^2=g_(11)(dx^1)^2+g_(22)(dx^2)^2+g_(33)(dx^3)^2.

At ordinary points on a surface, the line element is positive definite.

See also

Area Element, Fundamental Forms, Minkowski Metric, Volume Element

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Cite this as:

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

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