Arithmetic Billiards
In recreational mathematics, arithmetic billiards provide a geometrical method to determine the least common multiple (LCM) and the greatest common divisor (GCD) of two Natural number, natural numbers. It makes use of reflections inside a rectangle that has sides with length of the two given numbers. This is a simple example of trajectory analysis used in dynamical billiards. Arithmetic billiards can be used to show how two numbers interact. Drawing squares within the rectangle of length and width of the two natural numbers allows a reader to learn more about the relationship between the two numbers. Coprime integers interact with every unit square within the rectangle. Properties Arithmetic billiards is a name given to the process of finding both the LCM and the GCD of two integers using a geometric method. It is named for its similarity to the movement of a billiard ball. To create an arithmetic billiard, a rectangle is drawn with a base of the larger number, and height of ...
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