CrossRatio - Maple Help

geometry

 CrossRatio
 compute the cross ratio (or anharmonic ratio, or double ratio) of four points

 Calling Sequence CrossRatio(A, B, C, F)

Parameters

 A, B, C, F - four points

Description

 • Given four points A, B, C, F, the routine CrossRatio(A, B, C, F) computes the cross ratio of A, B, C, F taken in this order.
 • If A, B, C, F are four distinct points on an ordinary line, the cross ratio of A, B, C, F taken in this order is defined as:

$\frac{\frac{\mathrm{SensedMagnitude}\left(A,C\right)}{\mathrm{SensedMagnitude}\left(C,B\right)}}{\frac{\mathrm{SensedMagnitude}\left(A,F\right)}{\mathrm{SensedMagnitude}\left(F,B\right)}}$

 • The command with(geometry,CrossRatio) allows the use of the abbreviated form of this command.

Examples

 > $\mathrm{with}\left(\mathrm{geometry}\right):$
 > $\mathrm{point}\left(A,0,0\right),\mathrm{point}\left(B,3,3\right),\mathrm{point}\left(C,7,7\right),\mathrm{point}\left(F,\frac{21}{11},\frac{21}{11}\right):$
 > $\mathrm{CrossRatio}\left(A,B,C,F\right)$
 ${-}\frac{\sqrt{{98}}{}\sqrt{{32}}{}\sqrt{{882}}{}\sqrt{{288}}}{{28224}}$ (1)
 > $\mathrm{CrossRatio}\left(A,C,B,F\right)$
 $\frac{\sqrt{{18}}{}\sqrt{{32}}{}\sqrt{{882}}{}\sqrt{{6272}}}{{28224}}$ (2)