Periodic Trajectories in the Regular Pentagon, II
نویسندگان
چکیده
منابع مشابه
Periodic trajectories in the regular pentagon
The study of billiards in rational polygons and of directional flows on flat surfaces is a fast-growing and fascinating area of research. A classical construction reduces the billiard system in a rational polygon – a polygon whose angles are π-rational – to a constant flow on a flat surface with conical singularities, determined by the billiard polygon. In the most elementary case, the billiard...
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Consider all geodesics between two given points on a polyhedron. On the regular tetrahedron, we describe all the geodesics from a vertex to a point, which could be another vertex. Using the Stern– Brocot tree to explore the recursive structure of geodesics between vertices on a cube, we prove, in some precise sense, that there are twice as many geodesics between certain pairs of vertices than o...
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ژورنال
عنوان ژورنال: Moscow Mathematical Journal
سال: 2013
ISSN: 1609-3321,1609-4514
DOI: 10.17323/1609-4514-2013-13-1-19-32