Concept information
Término preferido
projective harmonic conjugate
Definición
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In projective geometry, the harmonic conjugate point of a point on the real projective line with respect to two other points is defined by the following construction:
- Given three collinear points A, B, C, let L be a point not lying on their join and let any line through C meet LA, LB at M, N respectively. If AN and BM meet at K, and LK meets AB at D, then D is called the harmonic conjugate of C with respect to A and B.
The point D does not depend on what point L is taken initially, nor upon what line through C is used to find M and N. This fact follows from Desargues theorem.
In real projective geometry, harmonic conjugacy can also be defined in terms of the cross-ratio as (A, B; C, D) = −1.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Projective_harmonic_conjugate)
Concepto genérico
etiqueta alternativa (skos)
- harmonic conjugate point
En otras lenguas
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francés
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conjugaison harmonique
URI
http://data.loterre.fr/ark:/67375/PSR-NFS3J16J-V
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