Fibonacci Plays Billiards
History and Overview
2020-02-11 v1 Number Theory
Abstract
A chain is an ordering of the integers 1 to n such that adjacent pairs have sums of a particular form, such as squares, cubes, triangular numbers, pentagonal numbers, or Fibonacci numbers. For example 4 1 2 3 5 form a Fibonacci chain while 1 2 8 7 3 12 9 6 4 11 10 5 form a triangular chain. Since 1 + 5 is also triangular, this latter forms a triangular necklace. A search for such chains and necklaces can be facilitated by the use of paths of billiard balls on a rectangular or other polygonal billiard table.
Cite
@article{arxiv.2002.03705,
title = {Fibonacci Plays Billiards},
author = {Elwyn Berlekamp and Richard K. Guy},
journal= {arXiv preprint arXiv:2002.03705},
year = {2020}
}