منابع مشابه
A note on isosceles planar graph drawing
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متن کاملIsosceles Sets
In 1946, Paul Erdős posed a problem of determining the largest possible cardinality of an isosceles set, i.e., a set of points in plane or in space, any three of which form an isosceles triangle. Such a question can be asked for any metric space, and an upper bound ( n+2 2 ) for the Euclidean space E was found by Blokhuis [3]. This upper bound is known to be sharp for n = 1, 2, 6, and 8. We wil...
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A set S of k points in the plane is a universal point subset for a class G of planar graphs if every graph belonging to G admits a planar straight-line drawing such that k of its vertices are represented by the points of S. In this paper we study the following main problem: For a given class of graphs, what is the maximum k such that there exists a universal point subset of size k? We provide a...
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We show how to associate a computation to certain 2 degree of freedom hamiltonian systems, and use this to discuss the level of complexity of certain problems in the dynamics of these systems. A type of Turing machine over the reals can be identified, embedded in these systems. 1.Introduction. In two articles [1], C.Moore has explored a class of simple dynamical systems, and, in particular, has...
متن کاملBilliards in Nearly Isosceles Triangles
We prove that any sufficiently small perturbation of an isosceles triangle has a periodic billiard path. Our proof involves the analysis of certain infinite families of Fourier series that arise in connection with triangular billiards, and reveals some self-similarity phenomena in irrational triangular billiards. Our analysis illustrates the surprising fact that billiards on a triangle near a V...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 1998
ISSN: 0179-5376
DOI: 10.1007/pl00009356