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## Tangent planes of a surface

Differential Geometry
Grigorios Kostakos
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### Tangent planes of a surface

Let $S$ be a regular surface in $\mathbb{R}^3$. Prove that if all the tangent planes of the surface passing through the origin, then the Gaussian curvature $K$ of $S$ must be zero everywhere.
Grigorios Kostakos