Definition:Cross-Ratio/Points on Line
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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
- 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