Geodesic
Circles of numbers
Glasgow mathematical journal, Tome 19 (1978) no. 2, pp. 115-119

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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. 
Burmester, M.; Forcade, R.; Jacobs, E. Circles of numbers. Glasgow mathematical journal, Tome 19 (1978) no. 2, pp. 115-119. doi: 10.1017/S0017089500003487
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