# 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.
2 Citations
“Sum” Visual Rearrangements of the Alternating Harmonic Series
• Mathematics
• The College Mathematics Journal
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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 areaExpand
A Dissection Proof of Euler′s Series for 1 – γ
Summary We demonstrate a visualization of Euler′s series for 1 – γ, where γ is the Euler–Mascheroni constant.

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