What's the largest pizza the Pope could order?
This was an idea that came about when ordering pizza with friends, where we didn't have a very large table to put all the pizza on. The question arose: how large a pizza could we order and have them all fit on the table? I don't remember the exact answer to that particular question, but I do recall where it went next: what's the limiting factor at a larger scale? How large a pizza could the citizens of a small, densely-populated country order and still have them all fit within the country area? As a fan of Randall Munroe's What If? this sort of 'apply maths to stupid question' problem appeals to me, so I had a go. The nesting of 2D shapes in an irregular planar area is a tricky subject, so to simplify, we'll consider any country to simply be a hexagon. Why hexagons? Because the most dense arrangement of circles on a plane is hexagonal close packing, or 'HCP'. ...