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Circles of numbers

Published online by Cambridge University Press:  18 May 2009

M. Burmester ,
R. Forcade  and
E. Jacobs
M. Burmester
Affiliation:
Department of Mathematics, Royal Holloway College, Egham, Surrey
R. Forcade
Affiliation:
1208 Major, Normal, Illinois
E. Jacobs
Affiliation:
Department of Mathematics, Illinois State University, Normal, Illinois
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Arrange any n integers around a circle. The following procedure can be used to obtain another circle of n integers. For each adjacent pair of the first integers, form the absolute value of their difference and place it between them; then remove the original numbers. This procedure can be repeated over and over. When n = 4 this always leads eventually to a circle of zeros. On the other hand when n = 3, unless the original numbers are equal, this never happens. We treat below the general case and related problems, using for convenience a slightly different formulation. Surprisingly there is enough structure to lead to some interesting mathematics.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 19 , Issue 2 , July 1978 , pp. 115 - 119
Copyright
Copyright © Glasgow Mathematical Journal Trust 1978