Clifford Point

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Clifford point P with associated triangles ABF , ACD , BCE and FDE as well as their perimeters

The Clifford point of four lines in general position is one of the remarkable points of Euclidean plane geometry . It is linked to the name of the British mathematician and philosopher William Kingdon Clifford .

The Clifford point is determined by Clifford's theorem :

If there are four straight lines of the Euclidean plane, three of which each form the side straight lines of a real triangle , then the associated four circles of these triangles have a common point.

literature

  • William Kingdon Clifford : Mathematical Papers . Chelsea Publishing Company, Bronx NY 1968.
  • HSM Coxeter : Immortal Geometry . Birkhäuser Verlag, Basel / Stuttgart 1963 (translated into German by JJ Burckhardt).
  • Eberhard M. Schröder: Geometry of Euclidean planes . Verlag Ferdinand Schöningh, Paderborn 1985, ISBN 3-506-78220-7 .

Individual evidence

  1. ↑ Eberhard M. Schröder: Geometry of Euclidean planes . Verlag Ferdinand Schöningh, Paderborn 1985, ISBN 3-506-78220-7 , p. 80 .
  2. ↑ HSM Coxeter : Immortal Geometry . Birkhäuser Verlag, Basel / Stuttgart 1963, p. 318–319 (translated into German by JJ Burckhardt).
  3. ^ William Kingdon Clifford : Mathematical Papers . Chelsea Publishing Company, Bronx NY 1968, pp. 51 .