Problem #37

Recall that the Cantor set is obtained by taking the unit interval [0,1] removing the "middle third" (namely the interval (1/3, 2/3)), then the two "middle thirds" of the remaining intervals (namely the intervals (1/9, 2/9) and (7/9, 8/9)), then the four "middle thirds", etc., etc., ad infinitum, as shown in the figure below.

This month's problem is to find the average distance between two points in the Cantor set.

Back to the Advanced Problem Archives

Back to the Math Department Homepage.