Summary edit

Description01-Dreizehneck.svg	Deutsch: Dreizehneck, Näherungskonstruktion English: Tridecagon, approximation
Date	31 March 2015
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.

Ergebnis edit

Bezogen auf den Einheitskreis r = 1 [LE] edit

• Konstruierte Seitenlänge des Dreizehnecks in GeoGebra ${\displaystyle s_{k}=0,478631328575087...\;[LE]}$
• Seitenlänge des Dreizehnecks ${\displaystyle s=r\cdot 2\cdot \sin \left({\frac {180^{\circ }}{13}}\right)=0,478631328575115534...\;[LE]}$
• Absoluter Fehler der konstruierten Seitenlänge = ${\displaystyle s_{k}-s=-2{,}85...E-14\;[LE]}$
• Konstruierter Zentriwinkel des Dreizehnecks in GeoGebra ${\displaystyle \alpha _{k}=27{,}6923076923115...^{\circ }}$
• Zentriwinkel des Dreizehnecks ${\displaystyle \alpha =\left({\frac {360^{\circ }}{13}}\right)=27{,}{\overline {692307}}^{\circ }}$
• Absoluter Winkelfehler vom konstruierten Zentriwinkel = ${\displaystyle \alpha _{k}-\alpha =3{,}80...E-12^{\circ }}$

Beispiel um den Fehler zu verdeutlichen edit

Bei einem Umkreisradius r = 100 Mio. km wäre der absolute Fehler der 1. Seite ca. -2,85 mm.

Result edit

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

• Constructed side lenght of tridecagon ${\displaystyle s_{k}=0.478631328575087...\;[unit\;of\;length]}$
• Side lenght of the tridecagon ${\displaystyle s=r\cdot 2\cdot \sin \left({\frac {180^{\circ }}{13}}\right)=0.478631328575115534...\;[unit\;of\;length]}$
• Absolute error of the constructed side lenght = ${\displaystyle s_{k}-s=-2.85...E-14\;[unit\;of\;length]}$
• Constructed central angle ${\displaystyle \alpha _{k}=27.6923076923115...^{\circ }}$
• Central angle of tridecagon ${\displaystyle \alpha =\left({\frac {360^{\circ }}{13}}\right)=27.{\overline {692307}}^{\circ }}$
• Absolute angular error of the constructed central angle = ${\displaystyle \alpha _{k}-\alpha =3.80...E-12^{\circ }}$

Example to illustrate the error edit

At a circumscribed circle radius r = 100 million km, the absolute error of the 1st side would be approximately -2.85 mm.

Licensing edit

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