Summary edit

Description01-Elfeck-Animation-2.gif	Deutsch: Elfeck, Animation einer Näherungskonstruktion English: Hendecagon, Animation of an approximate construction
Date	4 July 2016
Source	Own work
Author	Petrus3743
Other versions

Ergebnis edit

Bezogen auf den Einheitskreis r = 1 [LE] edit

• Konstruierte Seitenlänge des Elfecks in GeoGebra (Anzeige max. 15 Nachkommastellen) ${\displaystyle a=0{,}563465113682859\;[LE]}$
• Seitenlänge des Elfecks ${\displaystyle a_{SOLL}=r\cdot 2\cdot \sin \left({\frac {180^{\circ }}{11}}\right)=0{,}563465113682859\ldots \;[LE]}$
• 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 Elfecks in GeoGebra (Anzeige signifikante 13 Nachkommastellen) ${\displaystyle \mu =32{,}7272727272727^{\circ }}$
• Zentriwinkel des Elfecks ${\displaystyle \mu _{SOLL}=\left({\frac {360^{\circ }}{11}}\right)=32{,}{\overline {72}}^{\circ }}$
• Absoluter Winkelfehler vom konstruierten Zentriwinkel:

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. 55 min), wäre der absolute Fehler der konstruierten Seitenlänge < 1 mm.

Result edit

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

• Constructed side lenght of the hendecagon in GeoGebra (Display max 15 decimal places) ${\displaystyle a=0.563465113682859\;[unit\;of\;length]}$
• Side lenght of the hendecagon ${\displaystyle a_{target}=2\cdot \sin \left({\frac {180^{\circ }}{11}}\right)=0.563465113682859\ldots \;[unit\;of\;length]}$
• 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 hendecagon in GeoGebra (display significant 13 decimal places) ${\displaystyle \mu =32{,}7272727272727^{\circ }}$
• Central angle of the hendecagon ${\displaystyle \mu _{target}={\frac {360^{\circ }}{11}}=32{,}{\overline {72}}^{\circ }}$
• 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 55 minutes), the absolute error of the 1st side would be < 1 mm.

Weblinks edit

Wikibooks: Elfeck (Hendcagon) u. a. mit Konstruktionsbeschreibung, Hendcagon with description of the construction (German)]

Licensing edit

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