Catching Proteus: The Collaborations of Wallis and Brouncker. I. Squaring the Circle

William Brouncker (ca. 1620-1684) was the inaugural President of The Royal Society, and John Wallis (1616-1703) one of its founder members. The two collaborated closely during the 1650s on some original and unusual mathematics, but while Wallis acquired a lasting reputation, Brouncker's work is...

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Published inNotes and records of the Royal Society of London Vol. 54; no. 3; pp. 293 - 316
Main Author Stedall, Jacqueline A.
Format Journal Article
LanguageEnglish
Published London The Royal Society 2000
Royal Society of London
Subjects
Algebra
Circles
Continued fractions
Fractions
Hyperbolas
Mathematical notation
Numerical quadratures
Parabolas
Rectangles
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ISSN0035-9149
DOI10.1098/rsnr.2000.0114

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Summary:William Brouncker (ca. 1620-1684) was the inaugural President of The Royal Society, and John Wallis (1616-1703) one of its founder members. The two collaborated closely during the 1650s on some original and unusual mathematics, but while Wallis acquired a lasting reputation, Brouncker's work is no longer well known. The two parts of this paper analyse the joint work of Wallis and Brouncker and attempt to separate their respective contributions and very different mathematical styles. The main subject of Part I is Brouncker's discovery of continued fractions. He gave few clues as to how he obtained his results and I offer a possible reconstruction of his work. His quadrature of the hyperbola and rectification of the semicubical parabola are also discussed. Brouncker emerges as a skilled and intuitive mathematician.
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ISSN:0035-9149
DOI:10.1098/rsnr.2000.0114