The Convergence of Difference Boxes
This is a sample article from the May 2005 issue of The American Mathematical Monthly.
Abstract: We consider an elementary mathematical puzzle known as a “difference box” in terms of a discrete map from R4 to R4 or, canonically, from a subset of the first quadrant of R2 into itself. We identify the map’s unique canonical fixed point and answer more generally the question of how many iterations a given “difference box” takes to reach zero. (The number is finite except for boxes corresponding to the fixed
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