Algebra and Trigonometry 10th Edition

To divide a line into 2 equal parts it has to be bisected once and hence the midpoint formula is used 1 time. To divide a point into 4 equal parts, the midpoint formula is applied once each to the equal parts from before, giving a total three usages of the formula so far and 8 equal parts would then require 7 usages and so on. As can bee seen to divide a line into $2^{n}$ parts we require $2^{n-1}$ usages of the midpoint formula