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Mathematical Digest


Short Summaries of Articles about Mathematics
in the Popular Press

"Mathematical Devices for Getting a Fair Share," by Theodore P. Hill. American Scientist, July/August 2000, pages 325-331.

Is it possible to divide a ham and cheese sandwich into two equal pieces, each of which has the same amount of bread, cheese, and ham? As this article points out, the surprising answer is yes. Despite its whimsical name, the "Ham Sandwich Theorem" is an important element in the solution of many "fair division" problems in mathematics. These problems ask how an object can be divided up in such a way that all claimants receive a fair share. What each claimant considers "fair" could depend on what he or she values about the object being divided. For example, there are ways of dividing up a cake that insure that those who value frosting over cake are just as satisfied as those who value cake over frosting. As the article discusses, these problems can have important applications to real-world negotiations over disarmament or land.

--- Allyn Jackson