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Interetingly, I've concluded that cutting a pizza to 4 pieces makes the rim support the tip properly, regardless of the size of the pizza, while cutting the pizza to 8 pieces makes the tip of the piece always flop. However, one quadrant of the pizza is harder to eat, because it widens so radicaly. This has made me a believer of cutting the pizza to 6 pieces, as this solves both issues.
I woudn't be surprised if some maths genius would've calculated that the 5 pieces would be the most optimal for both issues, the tip support, and the edibility. However, cutting to 5 equal pieces is rather bothersom, so I'll be sticking with 6 pieces personally, regardless of what pizza enginers may have calculated.
Doesn't Costco do 6 pieces by default? That's always struck me as a good size.