What geometry theorem says alternating slices of a disk can have equal area?

The Pizza theorem says that alternating slices of a suitably divided disk can have equal total area.

Take a disk and choose an interior point that need not be its center. Draw equally angled sectors through that point, with the number of sectors a multiple of four and at least eight. If the sectors are numbered in order, the alternating odd-numbered and even-numbered groups have the same area. Thus, with eight slices, two people taking alternate pieces receive equal amounts of pizza even when the cuts do not meet at the center.

The result is surprising because slices near the off-center meeting point can look very different. The equality comes from the geometry of the paired sectors, not from visual symmetry. A multiple of four is important; four sectors or other counts generally do not guarantee equality.

The theorem concerns area, but related results show that crust can also be divided equally in the standard setup. It is often confused with the ham sandwich theorem, which concerns bisecting measures in higher-dimensional settings.