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Journal Article

A Dissection Proof of Leibniz’s Series for π⁄4

Mitsuo Kobayashi
Mathematics Magazine
Vol. 87, No. 2 (April 2014), pp. 145-150
DOI: 10.4169/math.mag.87.2.145
Stable URL: http://www.jstor.org/stable/10.4169/math.mag.87.2.145
Page Count: 6
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A Dissection Proof of Leibniz’s Series for π⁄4
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Abstract

Summary Inspired by Lord Brouncker’s discovery of his series for ln 2 by dissecting the region below the curve 1⁄x, Viggo Brun found a way to partition regions of the unit circle so that their areas correspond to terms of Leibniz’s series for π⁄4. Brun’s argument involved ad hoc methods which were difficult to find. We develop a method based on usual techniques in calculus that leads to Brun’s result and that applies generally to other related series.

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