Symmetry and Pattern in Projective Geometry by Eric Lord

Author:Eric Lord
Language: eng
Format: epub, pdf
Publisher: Springer London, London

(k is an arbitrary factor that allows the unit of length to be chosen) satisfies

and, for any three non-infinite collinear points A, B and C,

Hence we can define the length of a line segment AB to be (AB), the distance between any two points A and B as the absolute value |(AB)|. Observe that isotropic lines are lines of zero length—the distance between any two points on an isotropic line is zero.

For similar reasons, for any two lines a and b there are two tangents m and n to Q through their point of intersection and the angle between a and b can be defined by

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