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Discrete Laplace-Darboux sequences, Menelaus' theorem and the pentagram map

Schief, WK (TU Berlin)
Friday 03 April 2009, 09:30-10:15



The discrete analogue of the classical notion of Laplace-Darboux sequences of conjugate nets was introduced by Doliwa. In view of the associated classi cation problem, we take a fresh look at this topic and re-formulate the theory in terms of the multi-ratio condition associated with Menelaus' theorem. As an application, we demonstrate that the pentagram map analysed in detail by Ovsienko, Schwartz and Tabachnikov may be regarded as a particular Laplace-Darboux sequence leading to a (non-standard) discrete version of the Schwarzian Boussinesq equation.


[pdf ]


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