Vsauce

The Pizza Theorem

We’re all familiar with standard pizza slices – one center slice and two 45-degree cuts and you’re ready to party with 6 perfect slices. Throw in another cut and you’ve got 8.

But what if I told you that you can cut a pizza anywhere on its surface — not just across its diameter — and get a perfectly fair, shareable pizza for two people by assigning alternating slices? Prepare to witness the most delicious, unexpected presentation of mathematical beauty: a proof without words. And bring napkins.

*** LINKS ***

The Pizza Theorem
http://web.maths.unsw.edu.au/~mikeh/webpapers/paper57.pdf

Mathematics Magazine, Volume 41, 1968: “Problem 660” by L.J. Upton, Solution by Michael Goldberg: https://www.jstor.org/stable/2687962

Mathematics Magazine, Volume 67, 1994. “Proof without Words: Fair Allocation of a Pizza” by Larry Carter and Stan Wagon: https://www.jstor.org/stable/2690845

Dividing Thin Crust, Calzones, and Stuffed Crust Pizzas:
https://lsusmath.rickmabry.org/rmabry/pizza/Pizza_Conjecture.pdf

Exotic Mathematical Pizza Slicing: https://www.newscientist.com/article/dn28743-mathematicians-invent-new-way-to-slice-pizza-into-exotic-shapes/

Infinite Families Of Monohedral Disk Tilings: https://arxiv.org/pdf/1512.03794.pdf

Pizza Theorem Proof Without Words Calculator by Christian Lawson-Perfect: https://www.geogebra.org/m/C9kMuwj8

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