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How Bürgi computed the sines of all integer angles simultaneously in 1586

  • Mathematik in historischer und philosophischer Sicht
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Abstract

We present an algorithm discovered by Jost Bürgi around 1586, lost until 2013, and proven in 2015. Bürgi’s method needs only sums of integers and divisions by \(2\) to compute simultaneously and with any desired accuracy the sines of the \(n\)th parts of the right angle. We explain why it works with a new proof using polygons and discrete Fourier transforms.

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Notes

  1. And as, because of my lack of languages, the door to the authors wasn’t always open to me as it was to others, I had to follow my own thoughts and find new ways a little more than, for example, the scholars and well-read. Jost Bürgi, Introduction to Coss [13].

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Authors and Affiliations

  1. University of Applied Sciences of Western Switzerland, Route du Rawil 47, 1950, Sion, Switzerland

    Grégoire Nicollier

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  1. Grégoire Nicollier
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Correspondence to Grégoire Nicollier.

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We are very grateful to Jörg Waldvogel for his generous and fruitful introduction to the subject.

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Nicollier, G. How Bürgi computed the sines of all integer angles simultaneously in 1586. Math Semesterber 65, 15–34 (2018). https://doi.org/10.1007/s00591-017-0209-0

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