Definition:Harmonic Range

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 $AB$.


 * Harmonic-range.png

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.

Also see

 * Definition:Harmonic Conjugates