OFFSET

1,2

COMMENTS

The maxima occur when the points of reflection are arranged at the vertices of a regular n-gon and the ray (except entering and leaving) follows the edges and diagonals of the polygon.

LINKS

M. Oskar van Deventer, Point Mirror Reflection, in The Mathemagician and the Pied Puzzler edited by E. Berlekamp and T. Rodgers, A K Peters Publishers, 1999, pp. 245-251. google books.

FORMULA

For p prime, a(p)=p^2-p+1.

a(n) <= n^2-n+1. [Deventer eq (1)]

a(n) <= n^2-2*n+3 for even n [Deventer eq. (2)]

CROSSREFS

KEYWORD

more,nonn

AUTHOR

Henry Bottomley, Feb 22 2002

STATUS

approved