page_title: Arithmetic billiards
section_title: One generalisation
hierarchical_section_title: Arithmetic billiards / One generalisation
caption_attribution_description: English: Mathematical image of an arithmetic billiard. Example (of a periodic path) with the numbers 35 and 14.
context_page_description: In recreational mathematics, arithmetic billiards provide a geometrical method to determine the least common multiple and the greatest common divisor of two natural numbers by making use of reflections inside a rectangle whose sides are the two given numbers. This is an easy example of trajectory analysis of dynamical billiards.
  Arithmetic billiards have been discussed as mathematical puzzles by Hugo Steinhaus and Martin Gardner, and are known to mathematics teachers under the name 'Paper Pool'.
  They have been used as a source of questions in mathematical circles.
context_section_description: If we allow the starting point of the path to be any point in the rectangle with integer coordinates, then there are also periodic paths unless the rectangle sides are coprime. The length of any periodic path equals .
caption: A periodic path in the generalised arithmetic billiard with sides 35 and 14.
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