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Additive frieze patterns and multiplication tables

Published online by Cambridge University Press:  22 September 2016

G. C. Shephard
G. C. Shephard*
Affiliation:
University of East Anglia, Norwich NR4 7TJ
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Extract

A frieze pattern is an array of numbers arranged in staggered rows, like the bricks in a wall. In the case of a multiplicative frieze pattern the top and bottom rows consist entirely of ones, and for each ‘diamond’ of four elements

the unimodular rule

ad = bc + 1 (2)

holds. These frieze patterns have many curious properties, and for further details the reader is referred to the article Triangulated polygons and frieze patterns by J. H. Conway and H. S. M. Coxeter which appeared in Gazette 57, 87–94 and 175–183 (1973).

Information

Type
Research Article
Information
The Mathematical Gazette , Volume 60 , Issue 413 , October 1976 , pp. 178 - 184
Copyright
Copyright © Mathematical Association 1976

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