论文标题
斐波那契扮演台球
Fibonacci Plays Billiards
论文作者
论文摘要
链条是整数1至n的排序，使相邻对具有特定形式的总和，例如正方形，立方体，三角形数，五角形数量或纤维纳基数。例如4 1 2 3 5形成斐波那契链，而1 2 8 7 3 12 9 6 4 11 10 5形成三角形链。由于1 + 5也是三角形，因此后者形成了三角项链。通过在矩形或其他多边形台球上使用台球球的路径，可以促进对此类链条和项链的搜索。
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.
