Envelope (Solid Geometry)/Examples/Spheres with Centers on Sphere

Example of Envelope in context of Solid Geometry

Let $\SS$ be a sphere with radius $r$ with center at $O$.

Let $\FF$ be the set of spheres with radius $a$ whose centers all lie on the surface of $\SS$.

Then the envelope of $\FF$ consists of:

a sphere with radius $r + a$ with center at $O$

a sphere with radius $\size {r - a}$ with center at $O$.

Proof

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Sources

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