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

Nicollier, Grégoire (School of Engineering, HES-SO Valais-Wallis, HEI, HES-SO // University of Applied Sciences Western Switzerland)

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 nth parts of the right angle. We explain why it works with a new proof using polygons and discrete Fourier transforms.


Keywords:
Article Type:
scientifique
Faculty:
Ingénierie et Architecture
School:
HEI VS HES-SO Valais-Wallis - Haute Ecole d'Ingénierie
Institute:
Institut Systèmes industriels
Subject(s):
Ingénierie
Date:
2018
Pagination:
20 pages
Published in
Mathematische Semesterberichte
Numeration (vol. no.):
2018, 65, 1, pp. 15-34
DOI:
ISSN:
0720-728X
Embargo date::
2019-03-31
Appears in Collection:

Note: The file is under embargo until: 2019-03-31


 Record created 2018-07-10, last modified 2018-10-05

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