Corpus ID: 211068753

Fibonacci Plays Billiards

@article{Berlekamp2020FibonacciPB,
  title={Fibonacci Plays Billiards},
  author={Elwyn R. Berlekamp and Richard K. Guy},
  journal={arXiv: History and Overview},
  year={2020}
}
  • Elwyn R. Berlekamp, Richard K. Guy
  • Published 2020
  • Mathematics
  • arXiv: History and Overview
  • 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… CONTINUE READING

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