Definition:Cross-Ratio/Points on Line

Definition

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

The cross-ratio of $A$, $B$, $C$ and $D$, in that specific order, is defined as:

$\dfrac {AC / CB} {AD / DB}$

or equivalently:

$\dfrac {AC \cdot DB} {AD \cdot CB}$

It can be denoted:

$\set {A, B; C, D}$

Also known as

Some sources do not hyphenate cross-ratio, leaving it as: cross ratio.

Also see

• Definition:Harmonic Ratio

• Results about cross-ratios can be found here.

Sources

• 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