Summary edit

Description01-Elfeck-3.svg	Deutsch: Elfeck, Näherungskonstruktion English: Hendecagon, approximate construction
Date	30 March 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.

Näherungsonstruktion edit

• Die Methode ähnelt der des Dreizehnecks

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. 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 lenght of the hendecagon in GeoGebra (Display max 15 decimal places) ${\displaystyle a=0.563465113682859\;[unit\;of\;length]}$
• Side lenght of the hendecagon ${\displaystyle a_{should}=2\cdot \sin \left({\frac {180^{\circ }}{11}}\right)=0.563465113682859\ldots \;[unit\;of\;length]}$
• Absolute error of the constructed side length

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

• Constructed central angle of the hendecagon in GeoGebra (display significant 13 decimal places) ${\displaystyle \mu =32{,}7272727272727^{\circ }}$
• Central angle of the hendecagon ${\displaystyle \mu _{should}={\frac {360^{\circ }}{11}}=32{,}{\overline {72}}^{\circ }}$
• Absolute error of the constructed central angle

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

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.

Weblinks edit

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

Licensing edit

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