# A Dissection Proof of Leibniz's Series for π/4

@article{Kobayashi2014ADP, title={A Dissection Proof of Leibniz's Series for $\pi$/4}, author={Mits Kobayashi}, journal={Mathematics Magazine}, year={2014}, volume={87}, pages={145 - 150} }

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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Such a decomposition provides a proof without words that the series converges to the particular sum, and there are a variety of interesting diagrams in the literature showing series as area… Expand

A Dissection Proof of Euler′s Series for 1 – γ

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Summary We demonstrate a visualization of Euler′s series for 1 – γ, where γ is the Euler–Mascheroni constant.

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