1. The kissing number of the regular pentagon
- Author
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Zhao, Likuan and Xu, Junqin
- Subjects
- *
POLYGONS , *TRIANGLES - Abstract
Let
pn be an arbitrary regular polygon withn sides. What is the maximum numberk(pn) of congruent regular polygons(copies ofpn ) that can be arranged so that each touchespn but no two of them overlap? Youngs (Amer. Meth. Monthly 46 (1939) 20), Klamkin et al. (Math Mag. 68 (1995) 128) and others established thatk(p3) = 12 ,k(p4) = 8 , andk(p6) = 6 . Likuan Zhao (Discrete Math. 188 (1998) 293) established thatk(pn) = 6(n>6) . In this paper, we will establishk(p5) = 6 . Thus we prove the guess in Likuan Zhao and completely solve the kissing numbers of all regular polygons. [Copyright &y& Elsevier]- Published
- 2002
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