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Half-Silvered Mirrors and Wythoff's Game

Published online by Cambridge University Press:  20 November 2018

Horacio Porta and
Kenneth B. Stolarsky
Horacio Porta
Affiliation:
Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, Illinois, 61801
Kenneth B. Stolarsky
Affiliation:
Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, Illinois, 61801
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Abstract

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We propose the following problem. Given an array of vertical mirrors that simultaneously transmit and reflect, and a single incoming ray of light, describe the configuration of all light rays that are generated. We solve the problem here for a certain infinite configuration of mirrors; the solution involves the winning positions (a(n), b(n)) of Wythoff's game.

Keywords

10A3210A3510F2078A05Secondary 90D42

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 33 , Issue 1 , 01 March 1990, pp. 119 - 125
Copyright
Copyright © Canadian Mathematical Society 1990

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