Cross Ratio

Author

Eric W. Weisstein
November 1, 2005

This notebook downloaded from http://mathworld.wolfram.com/notebooks/PlaneGeometry/CrossRatio.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/CrossRatio.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Code

Distance[x_,y_]:=Sqrt[#.#&[(x-y)]]
CrossRatio[{a_,b_,c_,d_}]:=((Distance[a,c]Distance[b,d])/(Distance[a,d]Distance[b,c]))

Figures

Square

CrossRatio[(a#+{x0,y0})&/@{{0,0},{0,1},{1,1},{1,0}}]

CrossRatio[{{0,0},{0,1},{1,0},{1,1}}]

Rectangle

CrossRatio[{{0,0},{a,0},{a,b},{0,b}}]//Simplify

Equilateral Triangle

CrossRatio[{{-1/2,0},{1/2,0},{0,(Sqrt[3])/2},{0,(Sqrt[3])/6}}a]