Discrete Laplace-Darboux sequences, Menelaus' theorem and the pentagram map
AbstractThe discrete analogue of the classical notion of Laplace-Darboux sequences of conjugate nets was introduced by Doliwa. In view of the associated classication 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.
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