Description01-Siebeneck E-11.svg	Deutsch: Siebeneck, Näherungskonstruktion English: Heptagon, approximation construction
Date	4 June 2016
Source	Own work
Author	Petrus3743
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• Die Methode ähnelt der des Dreizehnecks

• Konstruierte Seitenlänge des Siebenecks in GeoGebra (Anzeige max. 15 Nachkommastellen) ${\displaystyle a=\mathrm{0,867767478235116}[LE]}$
• Seitenlänge des Siebenecks ${\displaystyle a_{SOLL}=2\cdot \sin \left(\frac{180^{\circ }}{7}\right)=\mathrm{0,867767478235116}\dots [LE]}$
• Absoluter Fehler der konstruierten Seitenlänge

Bis zu den max. angezeigten 15 Nachkommastellen ist der absolute Fehler ${\displaystyle F_a=a-a_{SOLL}=\mathrm{0,0}[LE]}$

• Konstruierter Zentriwinkel des Siebenecks in GeoGebra (Anzeige signifikante 13 Nachkommastellen) ${\displaystyle \mu =\mathrm{51,428571428571}{4}^{\circ }}$
• Zentriwinkel des Siebenecks ${\displaystyle {\mu }_{SOLL}=\frac{360^{\circ }}{7}=\mathrm{51,4285714285714}{\dots }^{\circ }}$
• Absoluter Fehler des konstruierten Zentriwinkels

Bis zu den angezeigten signifikanten 13 Nachkommastellen ist der absoluter Fehler ${\displaystyle F_{\mu }=\mu -{\mu }_{SOLL}=0^{\circ }}$

Bei einem Umkreisradius r = 1 Mrd. km (das Licht bräuchte für diese Strecke ca. 56 min), wäre der absolute Fehler der konstruierten Seitenlänge < 1 mm.

• The method is similar to that of the Tridecagon

• Constructed side length of the heptagon in GeoGebra (display max 15 decimal places) ${\displaystyle a=0.867767478235116[unitoflength]}$
• Side length of the heptagon ${\displaystyle a_{target}=2\cdot \sin \left(\frac{180^{\circ }}{7}\right)=0.867767478235116\dots [unitoflength]}$
• Absolute error of the constructed side length

Up to the max. displayed 15 decimal places is the absolute error ${\displaystyle F_a=a-a_{target}=0.0[unitoflength]}$

• Constructed central angle of the heptagon in GeoGebra (display significant 13 decimal places) ${\displaystyle \mu =51.4285714285714^{\circ }}$
• Central angle of the heptagon ${\displaystyle {\mu }_{target}=\frac{360^{\circ }}{7}=51.4285714285714{\dots }^{\circ }}$
• Absolute error of the constructed central angle

Up to the indicated significant 13 decimal places is the absolute error ${\displaystyle F_{\mu }=\mu -{\mu }_{target}=0^{\circ }}$

At a circumscribed circle radius r = 1 billion km (the light needed for this distance about 56 minutes), the absolute error of the 1st side would be < 1 mm.

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