Discrete & Computational Geometry

, Volume 36, Issue 3, pp 489–498 | Cite as

Some Incidence Theorems and Integrable Discrete Equations

  • Vsevolod E. Adler


Several incidence theorems of planar projective geometry are considered. It is demonstrated that generalizations of the Pascal theorem due to Mobius give rise to the double cross-ratio equation and the Hietarinta equation. The construction corresponding to the double cross-ratio equation is a reduction to a conic section of some planar configuration (203154). This configuration provides a correct definition of the multi-dimensional quadrilateral lattices on the plane.


Intersection Point Discrete Comput Geom Conic Section Quadrilateral Lattice Partial Difference Equation 
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Copyright information

© Springer 2006

Authors and Affiliations

  1. 1.Institut fur Mathematik, Technische Universitat Berlin, Str. des 17. Juni 136, 10623BerlinGermany

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