Definition:Harmonic Conjugates/Harmonic Range
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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
Two pairs of:
which are harmonic conjugates are also known as a conjugate pair.
Harmonic conjugates can also be said to be apolar.
Also see
- 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
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): cross-ratio
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): cross-ratio