2012 USAJMO Problems/Problem 4
Let be an irrational number with , and draw a circle in the plane whose circumference has length 1. Given any integer , define a sequence of points , , , as follows. First select any point on the circle, and for define as the point on the circle for which the length of arc is , when travelling counterclockwise around the circle from to . Supose that and are the nearest adjacent points on either side of . Prove that .
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