Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

 AreaElement

Source Notebook

Compute the area element for a surface

Contributed by: Wolfram Staff (original content by Eric W. Weisstein)

ResourceFunction["AreaElement"][s,{u,v}]

computes the area element for a surface s parametrized by u,v.

Details and Options

The area element for a surface is computed using the first fundamental form.

Examples

Basic Examples (2) 

Area element of a sphere:

In[1]:=
FullSimplify[ ResourceFunction["AreaElement"][ Entity["Surface", "Sphere"]["ParametricEquations"][a][u, v], {u, v}], a > 0 && Sin[v] > 0]
Out[1]=

Area element of a monkey saddle:

In[2]:=
FullSimplify[ ResourceFunction["AreaElement"][ Entity["Surface", "MonkeySaddle"]["ParametricEquations"][a][u, v], {u, v}], a > 0]
Out[2]=

Publisher

Enrique Zeleny

Version History

  • 1.0.0 – 06 April 2020

Source Metadata

  • Citation:
    • Gray, A., Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press, 1997.

License Information