Cutting the Cake

We have a square cake (that is, its horizontal cross-sections are congruent squares). It is frosted evenly on the four sides and the top. How can we cut the cake into n pieces so that all the pieces have equal amounts of cake and equal amounts of frosting?

Questions to consider

Can you solve the problem for n = 2? . . . n = 3? . . . n = 4?

How would you solve the problem if the cake were circular rather than square? Does a similar method work for the square cake?

Look carefully. Does your method for a circular cake have another interpretation in terms of distance along the perimeter of the cake?