Abstract
For one hundred years it has been known that the number π is transcendental and, consequently, that it is impossible to construct, with straight-edge and compass, a square with the same area as a given circle. (For some history, see [7].) In this article we show how a close examination of the origins of the circle-squaring problem can be used to motivate a version of it, due to Alfred Tarski. The new version is still unresolved, but there are a number of partial results. We survey some of these and indicate how one in particular can be applied in contemporary work on characterizations of Lebesgue measure.
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Wagon, S. Circle-squaring in the twentieth century. The Mathematical Intelligencer 3, 176–181 (1981). https://doi.org/10.1007/BF03022979
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DOI: https://doi.org/10.1007/BF03022979