Description01-Siebeneck-E-9.svg	Deutsch: Siebeneck, Näherungskonstruktion English: Heptagon, approximation construction
Date	24 January 2016
Source	Own work
Author	Petrus3743
Other versions
SVG development InfoField	The SVG code is valid.  This trigonometry was created with GeoGebra by Petrus3743.  This SVG trigonometry uses the path text method.

• Konstruierte Seite des Siebenecks ${\displaystyle s_k=\mathrm{0,867767469717624...}[LE]}$
• Seite des Siebenecks ${\displaystyle s=2\cdot \sin \left(\frac{180^{\circ }}{7}\right)=\mathrm{0,867767478235116...}[LE]}$
• Absoluter Fehler der konstruierten Seite = ${\displaystyle s_k-s=-\mathrm{8,517...}E-9[LE]}$
• Relativer Fehler der konstruierten Seite [%] = ${\displaystyle \frac{s_k-s}{s}\cdot 100\mathrm{\%}=\frac{\mathrm{0,867767469717624}-\mathrm{0,867767478235116}}{\mathrm{0,867767478235116}}\cdot 100\mathrm{\%}=-\mathrm{0,00000098}\mathrm{\%}}$
• Konstruierter Zentriwinkel des Siebenecks ${\displaystyle {\alpha }_k=\mathrm{51,42857088691416..}{.}^{\circ }}$
• Zentriwinkel des Siebenecks ${\displaystyle \alpha =\frac{360^{\circ }}{7}=\mathrm{51,42857142857142..}{.}^{\circ }}$
• Absoluter Fehler des konstruierten Zentriwinkels ${\displaystyle {\alpha }_f={\alpha }_k-\alpha =-\mathrm{0,541...}E-7^{\circ }}$

Bei einem Radius r = 1.000 km wäre der absolute Fehler der 1. Seite ca. -8,5 mm.

• Constructed side of the heptagon ${\displaystyle s_k=\mathrm{0.867767469717624...}[unitoflength]}$
• Side of the heptagon ${\displaystyle s=2\cdot \sin \left(\frac{180^{\circ }}{7}\right)=\mathrm{0.867767478235116...}[unitoflength]}$
• Absolute error of the constructed side = ${\displaystyle s_k-s=-\mathrm{8.517...}E-9[unitoflength]}$
• Relative error of the constructed side [%] = ${\displaystyle \frac{s_k-s}{s}\cdot 100\mathrm{\%}=\frac{0.867767469717624-0.867767478235116}{0.867767478235116}\cdot 100\mathrm{\%}=-0.00000098\mathrm{\%}}$
• Constructed central angle of the heptagon ${\displaystyle {\alpha }_k=\mathrm{51.42857088691416..}{.}^{\circ }}$
• Central angle of the heptagon ${\displaystyle \alpha =\frac{360^{\circ }}{7}=\mathrm{51.42857142857142..}{.}^{\circ }}$
• Absolute error of the constructed central angle ${\displaystyle {\alpha }_f={\alpha }_k-\alpha =-\mathrm{0.541...}E-7^{\circ }}$

At a circumscribed circle radius r = 1,000 km, the absolute error of the 1st side would be approximately -8.5 mm.

I, the copyright holder of this work, hereby publish it under the following license:

This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.

You are free:

• to share – to copy, distribute and transmit the work
• to remix – to adapt the work

Under the following conditions:

• attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
• share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.

https://creativecommons.org/licenses/by-sa/4.0CC BY-SA 4.0 Creative Commons Attribution-Share Alike 4.0 truetrue