Some incidence theorems and integrable discrete equations
Abstract
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 (203 154). This configuration provides a correct definition of the multidimensional quadrilateral lattices on the plane.
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