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Pulli kolam is a ubiquitous art form in south India. It involves drawing a line looped around a collection of dots (pullis) place on a plane such that three mandatory rules are followed: all line orbits should be closed, all dots are encircled and no two lines can overlap over a finite length. The mathematical foundation for this art form has attracted attention over the years. In this work, we propose a simple 5-step topological method by which one can systematically draw all possible kolams for any number of dots N arranged in any spatial configuration on a surface.
Abstract axiomatic formulation of mathematical structures are extensively used to describe our physical world. We take here the reverse way. By making basic assumptions as starting point, we reconstruct some features of both geometry and topology in
The first part of this article intends to present the role played by Thom in diffusing Smales ideas about immersion theory, at a time (1957) where some famous mathematicians were doubtful about them: it is clearly impossible to make the sphere inside
In this note, we present a compatibility test based on John Nashs game-theoretic notion of equilibrium strategy. The test must be taken separately by both partners, making it difficult for either partner alone to control the outcome. The mathematics
This article is an updated version of an entry of the Encyclopedia of Mathematics Education (2018). In the same time, it is the seed of the HAL collection DAD-MULTILINGUAL, constituted by the translation of this entry in various languages.The documen
We prove that any cyclic quadrilateral can be inscribed in any closed convex $C^1$-curve. The smoothness condition is not required if the quadrilateral is a rectangle.