Editing First fundamental form (section)

{{Short description|Inner product of a surface in 3D, induced by the dot product}}
In [[differential geometry]], the '''first fundamental form''' is the [[inner product]] on the [[tangent space]] of a [[surface (differential geometry)|surface]] in three-dimensional [[Euclidean space]] which is induced [[canonical form|canonically]] from the [[dot product]] of {{math|'''R'''<sup>3</sup>}}.  It permits the calculation of [[curvature]] and metric properties of a surface such as length and area in a manner consistent with the [[ambient space]].  The first fundamental form is denoted by the Roman numeral {{math|I}},
<math display="block">\mathrm{I}(x,y)= \langle x,y \rangle.</math>