Definition:Circle of Apollonius

Definition

Let $A, B$ be distinct points in the plane.

Let $\lambda \in \R_{>0}$ be a strictly positive real number.

Let $X$ be the locus of points in the plane such that:

$X A = \map \lambda {X B}$

Then $X$ is a circle of Apollonius.

Also known as

The circle of apollonius can be otherwise worded as Apollonius' circle.

Also see

• Circle of Apollonius is Circle

• Results about the circle of Apollonius can be found here.

Source of Name

This entry was named for Apollonius of Perga.

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Apollonius' circle
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Apollonius' circle (circle of Apollonius)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Apollonius' circle (circle of Apollonius)
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Apollonius' circle
• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): Apollonius' circle