Kobayashi, Mitsuo A dissection proof of Leibniz’s series for \(\pi /4\). (English) Zbl 1298.41044 Math. Mag. 87, No. 2, 145-150 (2014). 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 \(\pi /4\). 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. Cited in 2 Documents MSC: 41A58 Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) 26A06 One-variable calculus Keywords:Leibniz’s series PDFBibTeX XMLCite \textit{M. Kobayashi}, Math. Mag. 87, No. 2, 145--150 (2014; Zbl 1298.41044) Full Text: DOI