Euler Theorem on Curvature of Surface

Theorem

Let $S$ be a surface in space.

The principal directions of the curvature of $S$ are perpendicular to each other.

Proof

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Source of Name

This entry was named for Leonhard Paul Euler.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): curvature
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Euler's theorem: 2.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): curvature
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Euler's theorem: 2.