cross ratio

noun

Geometry.

1. a ratio relating four points in the real or complex plane.

Other Word Forms

• cross-ratio adjective

Word History and Origins

Origin of cross ratio¹

First recorded in 1880–85

Example Sentences

The identity of the locus of the A′s with the envelope of the a′s follows at once; moreover, a line meets the singular surface in four points having the same cross ratio as that of the four tangent planes drawn through the line to touch the surface.

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It is generated by the lines which cut the faces of a tetrahedron in a constant cross ratio, and therefore by those subtending the same cross ratio at the four vertices.

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The cross ratio of a range of four collinear points can now be defined as a number characteristic of that range.

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