File:01-Siebeneck E-11.svg

Summary[edit]

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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Näherungsonstruktion[edit]

• Die Methode ähnelt der des Dreizehnecks

Ergebnis[edit]

Bezogen auf den Einheitskreis r = 1 [LE][edit]

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

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

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

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

Beispiel um den Fehler zu verdeutlichen[edit]

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.

Approximate construction[edit]

• The method is similar to that of the Tridecagon

Result[edit]

Based on the unit circle r = 1 [unit of length][edit]

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

Up to the max. displayed 15 decimal places is the absolute error ${\displaystyle F_{a}=a-a_{target}=0.0\;[unit\;of\;length]}$

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

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

Example to illustrate the error[edit]

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.

Licensing[edit]

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Attribution: Petrus3743

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