Frosting Fairness, Finally!

Many of us are familiar with how to slice a cake ensuring equal sized slices for all.  But what about those of us who want an equal amount of frosting as well?!  This question is a classic with the problem solvers amongst us.  In 1975, Martin Gardner considered a square cake cut into 7 pieces in his Scientific American column.  More than a decade earlier, H.S.M. Coxeter posed the problem for a square cake sliced into 9 pieces as an exercise in his book, Introduction to Geometry.  Together, we will solve this problem for a square cake cut into 5 pieces, and investigate the other cake shapes for which the same procedure will produce slices with equal cake and frosting.