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  Heptadecagon of Carl Friedrich Gauss

* 1777 in Braunschweig
+ 1855 in Göttingen


Heptadecagon Stadtfriedhof Göttingen

mein Foto 2.9.2022

The "Nobell-Rondell", a heptadecagon (17-gon) erected in 2006, is showing panels for Alfred Nobel and eight Nobel Prize Laureates buried in the city cemetery (Stadtfriedhof) of Göttingen:
Manfred Eigen, Max Born, Otto Hahn, Adolf Windaus, Richard Zsigmondy, Walter Nernst, Max Planck, Max von Laue, Otto Wallach.

The formula for cos(360°/17) used by Gauss to construct a heptadecagon [1]:

On March 30, 1796, one month before his nineteenth birthday, Carl Friedrich Gauss made the first entry in his notebook:
„Pricipia quibus innititur sectio circuli, ac divisibilitas geometrica in septemdecim partes etc“ [2].

LibreOffice spreadsheet:

The formula includes
- integer numbers only
- square roots
- basic operations + - * / only
which all can be constructed by ruler and compass (details in [3]).

The graphical construction is also possible for n = 3, 5, 17, 257, 65537 (Fermat primes) [1]:


[1] Carl Friedrich Gauss "Disquisitiones Arithmeticae" eod books2ebooks, p. 662 item 365.

[2] Duane W. DeTemple: Carlyle Circles and the Lemoine Simplicity of Polygon Constructions; The American Mathematical Monthly, Volume 98, Issue 2, Feb. 1991, p. 97-108

Heptadecagon (Wikipedia)
[3] Hans Vollmayr: Gleiche Ecken und Kanten mit Zirkel und Lineal; in: "Wie der Blitz einschlägt, hat sich das Räthsel gelöst", Niedersächsische Staats- und Universitätsbibliothek Göttingen 2005, ISBN 3-930457-72-5, p. 90-104

J. Giesen

Sept. 2022