# Gaussian curvature (idea)

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Taking its name from the famous [German] mathematician [Gauss|Carl Friederich Gauss], the Gaussian [curvature] of a [surface] at a point is obtained by taking the inverse of the [geometric mean] (the square root of the product, in this case) of the principal [curvature radius|curvature radii] at that point.
In symbols: While other definitions of cuvature are possible and in use (e.g.: 2/(r+R), which uses the arithmetic mean) the Gaussian definition is one of the most used, as it enters several interesting properties, with [developable surface|developability] being perhaps one of the most important.
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