Definition:Envelope/Solid Geometry

Definition

An envelope is a surface which is tangent to every element of a given set of surfaces.

Examples

Spheres with Centers on Sphere

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 $O$.

Also see

• Results about envelopes can be found here.

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.