Some incidence theorems and integrable discrete equations

Details Some incidence theorems and integrable discrete equations Some incidence theorems and integrable discrete equations

2004-09-30

arxiv.org/abs/nlin/0409065v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

12 p, 7 fig

Scientific paper

Several incidence theorems of planar projective geometry are considered. It is demonstrated that generalizations of Pascal theorem due to M\"obius give rise to double cross-ratio equation and Hietarinta equation. The construction corresponding to the double cross-ratio equation is a reduction to a conic section of some planar configuration $(20_3 15_4)$. This configuration provides a correct definition of the multidimensional quadrilateral lattices on the plane.

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