The Pentagonal Pizza Conjecture

The pentagonal pizza conjecture says that it is impossible to cut a pentagonal pizza into eight slices by four concurrent straight lines that make four equal smaller angles alternating with four equal bigger angles, and such that all smaller angle slices have the same area and all bigger angle slices have the same area. The conjecture is proved to be true when the pizza is shaped as an ellipse, triangle, or quadrilateral, except for a square, and is proved not true for all n-gons, where n >= 6. These results are closely related to the first theorem of convex geometry, Zindler's theorem of 1920. Similar results are proved for perimeter instead of area.

Automated summary

The pentagonal pizza conjecture states the difficulty of cutting a pentagonal pizza into eight slices under certain conditions. It has been proven true for ellipses, triangles, and quadrilaterals, excluding squares, but not true for polygons with six or more sides. These results are closely related to Zindler's 1920 theorem in convex geometry. Similar conclusions can be drawn when considering perimeter instead of area.