Plane Section of Spheroid Perpendicular to Axis of Revolution is Circle

Theorem

Let $\SS$ be a spheroid.

Let $\PP$ be a plane section of $\SS$ such that $\PP$ is perpendicular to the axis of revolution of $\SS$.

Proof

A spheroid is defined as the solid of revolution formed by rotation of an ellipse about one of its axes.

Hence the result by definition of solid of revolution.

$\blacksquare$

Sources

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