The arithmetic billiard for the numbers 15 and 40: the greatest common divisor is 5, the least common multiple is 120.
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[1] and Martin Gardner,[2] and are known to mathematics teachers under the name 'Paper Pool'.[3]
They have been used as a source of questions in mathematical circles.[4]
^Steinhaus, Hugo (1999). Mathematical Snapshots (Dover Recreational Math Series ed.). Courier Corporation. p. 63. ISBN 0486409147.
^Gardner, Martin (1984). Sixth Book of Mathematical Diversions from "Scientific American". University of Chicago Press. pp. 211–215. ISBN 0226282503.
^"Paper Pool Game". NCTM Illuminations. National Council of Teachers of Mathematics. Retrieved 10 January 2018.
^Tanton, James (2012). Mathematical Galore! The First Five Years of the St. Mark's Institute of Mathematics. The Mathematical Association of America. pp. 145–156. ISBN 978-0883857762.
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