A billiard ball is resting on a table that measures 10 feet by 5 feet. A player hits it with no “English” and it strikes four different cushions and returns to its starting point. University of Alberta mathematician Murray Klamkin asks: How far did it travel?
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The ball’s path can be drawn as a straight line (green) across a field of mirrored tables. It strikes four cushions and returns to its original position on the table. Its starting and ending positions (the endpoints of the green line) can be connected to a corner of the table by lines that are parallel and equal (yellow). If we complete the parallelogram (blue), it becomes clear that the ball’s path is equal in length to two of the table’s diagonals, or about 22.36 feet.
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