Definition:Gaussian Curvature

Definition

The Gaussian curvature $\Kappa$ of a surface at a point is the product of the principal curvatures, $\kappa_1$ and $\kappa_2$, at the given point:

$\Kappa = \kappa_1 \kappa_2$

Also known as

The Gaussian curvature is also known as the Gauss curvature.

Source of Name

This entry was named for Carl Friedrich Gauss.

Historical Note

The concept of Gaussian curvature was developed by Carl Friedrich Gauss in his $1827$ work Disquisitiones Generales circa Superficies Curvas.

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Gaussian curvature
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Gaussian curvature
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Gaussian curvature