How do you cut a circle into eight pieces with three cuts?

According to Programmer Interview, the circle must be cut into quarters using the first two cuts, and then the quarters must be stacked into one pile before making the last cut. This is done by stacking the pieces of the circle.

This is a bit of a trick question, and it is meant to make the solver think outside of the box. Step by step, the process is:

1. The circle is cut in half lengthwise with the first cut
2. The circle is cut vertically with the second cut, leaving four pieces of the circle (quarters)
3. The four pieces of the circle are stacked in a pile four high
4. The circle is cut in half with a final cut, leaving eight pieces