Definition:Harmonic Range

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

Definition

Let $A$ and $B$ be points on a straight line.

Let $P$ and $Q$ lie on $AB$ such that $P$ is on the line segment $AB$ while $Q$ is outside the line segment $AB$.

Let $P$ and $Q$ be positioned such that:

$\dfrac {AP} {PB} = -\dfrac {AQ} {QB}$

Then $\tuple {AB, PQ}$ are said to be a harmonic range.

Let $\tuple {AB, PQ}$ be a harmonic range such that $P$ is the midpoint of $AB$.