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# Mathematics > History and Overview

# Title: Fibonacci Plays Billiards

(Submitted on 4 Feb 2020)

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.

## Submission history

From: Richard K. Guy [view email] [via RENATE proxy]**[v1]**Tue, 4 Feb 2020 21:33:14 GMT (15kb)

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