Editing Heptagon (section)

===Approximation===
An approximation for practical use with an error of about 0.2% is to use half the side of an equilateral triangle inscribed in the same circle as the length of the side of a regular heptagon. It is unknown who first found this approximation, but it was mentioned by [[Heron of Alexandria]]'s ''Metrica'' in the 1st century AD, was well known to medieval Islamic mathematicians, and can be found in the work of [[Albrecht Dürer]].<ref>{{cite journal |title=Abu'l-Jūd's Answer to a Question of al-Bīrūnī Concerning the Regular Heptagon |last=Hogendijk |first=Jan P. |year=1987 |journal=Annals of the New York Academy of Sciences |volume=500 |issue=1 |url=https://www.jphogendijk.nl/publ/Abuljud.pdf |pages=175–183 |doi=10.1111/j.1749-6632.1987.tb37202.x}}</ref><ref>G.H. Hughes, [https://arxiv.org/ftp/arxiv/papers/1205/1205.0080.pdf#12 "The Polygons of Albrecht Dürer-1525, The Regular Heptagon", Fig. 11] [https://arxiv.org/ftp/arxiv/papers/1205/1205.0080.pdf#15 the side of the Heptagon (7) Fig. 15, image on the left side], retrieved on 4 December 2015</ref> Let ''A'' lie on the circumference of the circumcircle. Draw arc ''BOC''. Then <math>\scriptstyle {BD = {1 \over 2}BC}</math> gives an approximation for the edge of the heptagon.

This approximation uses <math>\scriptstyle {\sqrt{3} \over 2} \approx 0.86603 </math> for the side of the heptagon inscribed in the unit circle while the exact value is <math>\scriptstyle 2\sin{\pi \over 7} \approx 0.86777</math>.

''Example to illustrate the error:<br />
At a circumscribed circle radius ''r = 1&nbsp;m'', the absolute error of the 1st side would be ''approximately -1.7&nbsp;mm''

[[File:7-gone approx.png|240px]]