![]() ![]() The path of the billiard ball consists of line segments. It does not lose speed and, by the law of reflection, is reflected at a 45 degree angle each time it meets a side (thus the path only makes left or right 90 degree turns). The billiard ball bounces off the rectangle’s sides. We shoot a billiard ball from one corner (the bottom left in the figure above) making a 45 degree angle with the sides. ![]() For the billiard table we take a rectangle whose sides have lengths and. Suppose we are given two positive whole numbers and, neither of which is a multiple of the other (the case where one is a multiple of the other is easy and is left to the reader). The least common multiple of 40 and 15 equals 120, and the The two natural numbers are 40 and 15 in this case. If you would like to play the animation again, double click the refresh button in the top right corner. Have a look at the Geogebra animation below (the play button is in the bottom left corner)Īnd try to figure out how the construction works. Greatest common divisor of two natural numbers. Us a geometrical method to determine the least common multiple and the One fascinating aspect of mathematical billiards is that it gives This means that the ball willīounce infinitely many times on the sides of the billiard table and keep going forever. In mathematical billiards the ballīounces around according to the same rules as in ordinary billiards,īut it has no mass, which means there is no friction. Mathematical billiards is an idealisation of what weĮxperience on a regular pool table.
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