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Projective Geometry

Cross Ratio

Projections do not keep distances constant, nor do they enlarge or shrink them in an obvious way. In Figure 2, for instance, D'C' is a little smaller than CD, but A'B' is much larger than AB. There is, however, a rather obscure constancy about a projection's effect on distance. It is known as the "cross ratio." If A, B, C, and D are points in order on a line and if they are projected through a point P into points A', B', C', and D' on another line, then the two expressions and are equal.

Cross rations play an important part in many of projective geometry's theorems.

J. Paul Moulton

Additional topics

Science EncyclopediaScience & Philosophy: Positive Number to Propaganda - World War IiProjective Geometry - Desargues' Theorem, Coordinate Projective Geometry, Cross Ratio