Definition:Harmonic Conjugates/Harmonic Range

This page is about Harmonic Conjugates. For other uses, see Harmonic.

Definition

Let $AB$ and $PQ$ be line segments on a straight line such that $\tuple {AB, PQ}$ is a harmonic range.

Then $P$ and $Q$ are said to be harmonic conjugates with respect to $A$ and $B$.

Also known as

The two pairs of points $\set {A, B}$ and $\set {P, Q}$ can also be said to be apolar.

Also see

• Definition:Harmonic Range

• Results about Harmonic Ranges can be found here.

Sources

• 1933: D.M.Y. Sommerville: Analytical Conics (3rd ed.) ... (previous) ... (next): Chapter $\text {II}$. The Straight Line: $19$. Harmonic ranges and pencils