# Tangent plane

From Encyclopedia of Mathematics

*to a surface at a point *

The plane passing through characterized by the property that the distance from this plane to a variable point of as approaches arbitrarily close to is infinitesimally small as compared to the distance . If is given by an equation , then the equation of the tangent plane at a point , where , has the form

if and only if has a total differential at the point . In this case, and are the values of the partial derivatives and at .

#### Comments

For references see Tangent line.

**How to Cite This Entry:**

Tangent plane.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Tangent_plane&oldid=14114

This article was adapted from an original article by BSE-3 (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article