Alfred S. Posamentier and Robert Geretschlager, The Circle: A Mathematical Exploration Beyond the Line (Prometheus Books, 2016) goes considerably beyond what its modest title would suggest. The circle has played a pivotal role–that’s “role” with an ‘e,’ but its ability to “roll” with an ‘l’–has helped produce our industrial civilization. Moreover, the circle appears in our art, our literature, and our culture as well. This delightful book will not only reacquaint readers with the pleasures of the geometry they once knew, but will show how the circle continues to enchant mathematicians today, who continue to discover new and surprising properties about this most fundamental of shapes.

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