Mathematische Semesterberichte

, Volume 65, Issue 1, pp 15–34 | Cite as

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

  • Grégoire Nicollier
Mathematik in historischer und philosophischer Sicht


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.


Jost Bürgi Sine table Discrete Fourier transformation Finite difference Planar polygon Napoleon’s theorem Petr–Douglas–Neumann theorem 


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Copyright information

© Springer-Verlag GmbH Deutschland 2017

Authors and Affiliations

  1. 1.University of Applied Sciences of Western SwitzerlandSionSwitzerland

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