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 ElementExplore with Wolfram|Alpha
WolframAlpha
More things to try:
Cite this as:
Weisstein, Eric W. "Line Element." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LineElement.html