Definition:Harmonic Conjugates/Also known as

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

Harmonic Conjugates: Also known as

Two pairs of:

points $\set {A, B}$ and $\set {P, Q}$

rays $\set {OA, OB}$ and $\set {OP, OQ}$

which are harmonic conjugates are also known as a conjugate pair.

Harmonic conjugates can also be said to be apolar.

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): conjugate pair
• 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): conjugate pair
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): cross-ratio