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Fermat’s last pepperoni

13 December 2009 · 4:48 pm · Filed under Worth a Fork

Okay, nothing quite so startling as that. On the other hand, some day you’ll order a pizza, and this will matter to you:

Suppose the harried waiter cuts the pizza off-centre, but with all the edge-to-edge cuts crossing at a single point, and with the same angle between adjacent cuts. The off-centre cuts mean the slices will not all be the same size, so if two people take turns to take neighbouring slices, will they get equal shares by the time they have gone right round the pizza — and if not, who will get more?

And so there evolved a Unified Theorem of Pizza, which states the following:

[I]f you cut a pizza through the chosen point with an even number of cuts more than 2, the pizza will be divided evenly between two diners who each take alternate slices.

Otherwise:

[I]f you cut the pizza with 3, 7, 11, 15… cuts, and no cut goes through the centre, then the person who gets the slice that includes the centre of the pizza eats more in total. If you use 5, 9, 13, 17… cuts, the person who gets the centre ends up with less.

If you have $20 to spare, you could download the complete mathematical proof, or you could order a pretty darn big pizza. Make sure you tell them not to slice it.

(Via Jenn1964.)

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6 comments

  1. Jeffro »

    13 December 2009 · 8:37 pm

    Ahh, but what happens to the unfortunate pepperoni that would invariably be at the locus of all the edge to edge cuts?

  2. CGHill »

    13 December 2009 · 8:38 pm

    I am sure the researchers will see that it is disposed of in a non-wasteful manner.

  3. Da Goddess »

    14 December 2009 · 6:19 am

    I just make sure I get the few pieces I want and leave the rest for my minions to fight over.

    Is that wrong?

  4. Jeff Shaw »

    14 December 2009 · 1:22 pm

    I always have them cut the pizza in 8 slices. I don’t think I could eat 10 slices. (Insert optional spit take or rimshot, HERE).

  5. CGHill »

    14 December 2009 · 1:30 pm

    Now I feel better about requesting six slices on a Small.

  6. FMJRA Saturday again - « A Conservative Shemale »

    19 December 2009 · 5:58 am

    [...] links regarding the Unified Theory of Pizza Cutting. He seems to think it has practical applications. I think this is what I pay Dominos [...]

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