# Kunstweg

> Mediated Wiki article. Canonical URL: https://mediated.wiki/source/Kunstweg
> Markdown URL: https://mediated.wiki/source/Kunstweg.md
> Source: https://en.wikipedia.org/wiki/Kunstweg
> Source revision: 1345868745
> License: Creative Commons Attribution-ShareAlike 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/)

{{Use mdy dates|date=February 2016}}
thumb|300x300px|The ''Kunstweg'' by Jost Bürgi in his ''Fundamentum Astronomiae''.
Bürgi's '''Kunstweg''' is a set of [algorithm](/source/algorithm)s developed by [Jost Bürgi](/source/Jost_B%C3%BCrgi) in the late 16th century.<ref name="staudacher">Staudacher, S., 2014.  Jost Bürgi, Kepler und der Kaiser.  Verlag NZZ, Zürich.</ref> They are used to calculate [sines](/source/sines) to arbitrary precision.. Bürgi used these algorithms to calculate a [Canon Sinuum](/source/Canon_Sinuum_(B%C3%BCrgi)), a sine table in increments of 2 [arc seconds](/source/arc_seconds). It is believed that the table featured values accurate to eight sexagesimal places. Some authors have speculated that the table only covered the range from 0° to 45°, although there is no evidence supporting this claim. Such tables were crucial for maritime [navigation](/source/navigation). [Johannes Kepler](/source/Johannes_Kepler) described the Canon Sinuum as the most precise sine table known at the time.<ref>Max Caspar, ''Johannes Kepler Gesammelte Werke'', Band XVIII, page 149-150, Letter from Kepler to Landgraf Philipp von Hessen, december 1623. [https://kepler.badw.de/kepler-digital.html Bayerische Akademie der Wissenschaften]</ref> Bürgi explained his algorithms in his work ''[Fundamentum Astronomiae](/source/Fundamentum_Astronomiae)'', which he presented to [Emperor Rudolf II](/source/Emperor_Rudolf_II) in 1592.

The Kunstweg algorithm calculates sine values iteratively. In each step, the value of a cell is the sum of the two preceding cells in the same [column](/source/column). The final cell's value is halved before beginning the next iteration. Ultimately, the values in the last column are normalized. Accurate sine [approximations](/source/approximations) are achieved after only a few iterations.

In 2015, [Menso Folkerts](/source/Menso_Folkerts) and coworkers demonstrated that this iterative process does indeed converge toward the true sine values.<ref name="folkerts">{{citation
 | last1 = Folkerts | first1 = Menso | authorlink1=Menso Folkerts 
 | last2 = Launert | first2 = Dieter
 | last3 = Thom | first3 = Andreas |authorlink3=Andreas Thom (mathematician)
 | arxiv = 1510.03180
 | doi = 10.1016/j.hm.2016.03.001
 | issue = 2
 | journal = [Historia Mathematica](/source/Historia_Mathematica)
 | mr = 3489006
 | pages = 133–147
 | title = Jost Bürgi's method for calculating sines
 | volume = 43
 | year = 2016}}</ref> According to them this was the first step towards  [differential calculus](/source/difference_calculus).

== References ==
{{Reflist}}

{{DEFAULTSORT:Kunstweg (Jost Burgi)}}
Category:Algorithms
Category:Trigonometry

---
Adapted from the Wikipedia article [Kunstweg](https://en.wikipedia.org/wiki/Kunstweg) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Kunstweg?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.