Function Repository Resource:

# GaussianCurvature

Compute the Gaussian curvature of a surface

Contributed by: Alfred Gray
 ResourceFunction["GaussianCurvature"][s,{u,v}] computes the Gaussian curvature of the surface s parameterized by u and v. ResourceFunction["GaussianCurvature"][eq,{x,y,z}] computes the Gaussian curvature of the surface s given by the implicit equation eq in variables x,y and z.

## Details and Options

The Gaussian curvature is an intrinsic property of a space independent of the coordinate system used to describe that space.

## Examples

### Basic Examples (1)

Compute the Gaussian curvature of a sphere:

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### Scope (3)

Plot an astroidal ellipsoid:

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Now compute its Gaussian curvature:

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Plot the Gaussian curvature:

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Define a Möbius strip:

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Compute the Gaussian curvature:

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Plot the Gaussian curvature:

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Plot the Möbius strip colored according to its Gaussian curvature:

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Here is an implicit equation for a surface:

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Plot it:

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Compute its Gaussian curvature:

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### Properties and Relations (3)

The curvature can be obtained for named surfaces using entities:

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Here is the result returned by GaussianCurvature:

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The expressions seem to be different, but they are equal:

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Enrique Zeleny

## Version History

• 2.1.0 – 04 January 2021
• 2.0.0 – 01 April 2020
• 1.0.0 – 13 February 2020