Contest February 2012: Euclid's Cake

The February contest has ended.

At a children's birthday party, Euclid serves a circular cake and asks the children to cut the cake into a finite number of equal and continuous pieces. The only condition he insists on is that at least one piece must not touch the center point.

So the usual way of cutting a cake into pieces, as shown in the figure to the right, is not allowed, as all of the pieces touch the center here.

Equal means that all of the pieces must have the same shape and size. Reflections are allowed.

The solution can be found here.