The mathematics of pizza-sharing

The mathematics of pizza-sharing

Posted by Adam Kuban, December 13, 2009 at 4:00 PM

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[Photograph: Adam Kuban]

What happens when a pizza is not sliced exactly through the center? If you’re trying to share it equally, who will get the most crusty, saucy, cheesy goodness? From New Scientist:

Their quest started in 1994, when Deiermann showed Mabry a revised version of the pizza problem, again published in Mathematics Magazine (vol 67, p 304). Readers were invited to prove two specific cases of the pizza theorem. First, that if a pizza is cut three times (into six slices), the person who eats the slice containing the pizza’s centre eats more. Second, that if the pizza is cut five times (making 10 slices), the opposite is true and the person who eats the centre eats less.

The first statement was posed as a teaser: it had already been proved by the authors. The second statement, however, was preceded by an asterisk – a tiny symbol which, in Mathematics Magazine, can mean big trouble. It indicates that the proposers haven’t yet proved the proposition themselves. “Perhaps most mathematicians would have thought, ‘If those guys can’t solve it, I’m not going to look at it.'” Mabry says. “We were stupid enough to look at it.”

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