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.


Mots-clés:
Type d'article:
scientifique
Faculté:
Ingénierie et Architecture
Ecole:
HEI VS HES-SO Valais-Wallis - Haute Ecole d'Ingénierie
Institut:
Institut Systèmes industriels
Classification:
Ingénierie
Date:
2018
Pagination:
20 pages
Publié dans
Mathematische Semesterberichte
Numérotation (vol. no.):
2018, 65, 1, pp. 15-34
DOI:
ISSN:
0720-728X
Date d'embargo:
2019-03-31
Le document apparaît dans:

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


 Notice créée le 2018-07-10, modifiée le 2018-10-05

Fichiers:
Télécharger le document
PDF

Évaluer ce document:

Rate this document:
1
2
3
 
(Pas encore évalué)