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Recreational Problems in Medieval Mathematics

Victor J. Katz (University of the District of Columbia)


Recreational problems have been a fixture in mathematics problem solving from antiquity. It has long been known that the same problems reappear in cultures all over the world – from ancient Egypt and Babylonia through Greece, medieval China and India, and on into medieval Europe and the Renaissance, as well as modern times. What is surprising, perhaps, is that often the exact same problems reappear, even with the same numerical values, in cultures separated by hundreds of years and thousands of miles. For many years, David Singmaster has been gathering a data base of common recreational problems, a database which is now huge [Singmaster, 1996]. Similarly, there was an earlier book by Johannes Tropfke [Tropfke, 1980] that mentioned many of these problems from different cultures.

In this article, we will consider some appearances of two of these classic recreational problem types in sources not mentioned either by Singmaster or Tropfke. And then we will speculate a bit about the paths these problems traveled.

Victor J. Katz (University of the District of Columbia), "Recreational Problems in Medieval Mathematics," Convergence (December 2017)