# 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*.