Principal Normal on Geodesic Coincides with Normal to Surface

Theorem

Let $S$ be a surface.

Let $G$ be a geodesic on $S$.

Let $P$ be a point on $G$.

Then the principal normal to $G$ at $P$ coincides with the normal to $S$.

Proof

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Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): geodesic
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): geodesic