Difference between revisions of "Two-Pancake Problem"
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(I'd never heard of the two-dimensional version!) |
(Rewrote a portion of the article; the title is the PROBLEM. The article is about the THEOREM.) |
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| − | The '''Two-Pancake Problem''' is an introductory | + | The '''Two-Pancake Problem''' is an introductory problem in [[topology]] that asks whether two pancakes can be bisected with a single cut. The solution generates a theorem, called the '''Two-Pancake Theorem''', that the area of any two pancakes having an arbitrary two-dimensional shape can both be perfectly bisected with one straight line (one cut of a knife). Its proof is an illustration of the properties of continuous functions. It is the two-dimensional version of the three-dimensional [[Ham Sandwich Theorem]]. |
[[Category:mathematics]] | [[Category:mathematics]] | ||
[[Category:topology]] | [[Category:topology]] | ||
Revision as of 22:59, August 19, 2011
The Two-Pancake Problem is an introductory problem in topology that asks whether two pancakes can be bisected with a single cut. The solution generates a theorem, called the Two-Pancake Theorem, that the area of any two pancakes having an arbitrary two-dimensional shape can both be perfectly bisected with one straight line (one cut of a knife). Its proof is an illustration of the properties of continuous functions. It is the two-dimensional version of the three-dimensional Ham Sandwich Theorem.