Definition:Envelope/Plane Geometry

Definition

An envelope is a curve which is tangent to every element of a given set of curves.

Examples

Circles with Centers on Circle

Let $\CC$ be a circle with radius $r$ with center at $O$.

Let $\SS$ be the set of circles with radius $a$ whose centers all lie on the circumference of $\CC$.

Then the envelope of $\SS$ consists of:

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

a circle 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: 1.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): envelope: 1.