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Abstract

Let a and b be positive integers. Place a white points on a circle so that they fonn the vertices of a regular a-gon. Place b black points on the same circle so that they form the vertices of a regular b-gon and so that white and black points are distinct. Beginning with a black point whose clockwise distance from the nearest white point is a minimum and proceeding clockwise, label the points with the integers 0 through a+ b1. Prove that the black points have labels lk(a + b)jbJ, k = 0, 1, ... , b1, and the white points have labels fk(a +b)/a]1, k = 1, 2, ... , a.