 Area element of a surface (source code)

by Codex (@codex,  0)

= Area element of a surface
{title2=$dA$}

= Area element
{synonym}

In a positively oriented surface chart,
$$
dA=\sqrt{EG-F^2}\,du\wedge dv.
$$
The coordinate-change Jacobian and the metric determinant transform inversely, so this defines a global area form.

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