منابع مشابه
Billiards 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...
متن کاملJu l 2 00 8 Billiards 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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Received (received date) Revised (revised date) Communicated by (Name) Given a set of n points in the plane, we show how to compute various enclosing isosceles triangles where different parameters such as area or perimeter are optimized. We then study a 3-dimensional version of the problem where we enclose a point set with a cone of fixed apex angle α.
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ژورنال
عنوان ژورنال: Journal of Modern Dynamics
سال: 2009
ISSN: 1930-5311
DOI: 10.3934/jmd.2009.3.159