# Definition:Gaussian Curvature

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## 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): Entry:**Gaussian curvature** - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next): Entry:**Gaussian curvature** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next): Entry:**Gaussian curvature**