I was sitting down with Stefanie one day to share a round cake (our birthdays are only two weeks apart). "This is easy enough," I said, "one cut right through the middle divides the cake into two equal pieces."

Then, two more people showed up, but I was undaunted. Two straight cuts will divide the cake into four equal parts, I thought.

Then, I saw another car pulling up. I remembered that three straight lines can divide a circle into at most seven parts, but I was unsure if that could be done so that all the pieces are equal (in volume, not necessarily in shape).

How can I use three straight cuts to divide our cake into all equal parts and accomodate the greatest number of people?

Note: since Stefanie spent so much time decorating the cake, I don't want to rearrange the pieces when I cut them.