Summary

Description01-Dreizehneck-3 Animation.gif	Deutsch: Dreizehneck, Näherungskonstruktion als Animation, am Ende 15 s Pause English: Tridecagon, approximate construction as an animation, at the end 15 s pause
Date	18 March 2016
Source	Own work
Author	Petrus3743
Other versions

Ergebnis

Bezogen auf den Einheitskreis r = 1 [LE]

Tridecagon, approximate construction as an animation]]

• Konstruierte Seitenlänge des Dreizehnecks in GeoGebra (Anzeige max. 15 Nachkommastellen) ${\displaystyle a=0{,}478631328575115\;[LE]}$
• Seitenlänge des Dreizehnecks ${\displaystyle a=r\cdot 2\cdot \sin \left({\frac {180^{\circ }}{13}}\right)=0,478631328575115534...\;[LE]}$
• 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 Dreizehnecks in GeoGebra (Anzeige max. 14 Nachkommastellen) ${\displaystyle \mu =27{,}69230769230769^{\circ }}$
• Zentriwinkel des Dreizehnecks ${\displaystyle \mu _{SOLL}=\left({\frac {360^{\circ }}{13}}\right)=27{,}{\overline {692307}}^{\circ }}$
• Absoluter Winkelfehler vom konstruierten Zentriwinkel:

Bis zu den max. angezeigten 14 Nachkommastellen ist der absoluter Fehler ${\displaystyle F_{\mu }=\mu _{SOLL}-\mu =0^{\circ }}$

Beispiel um den Fehler zu verdeutlichen

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

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

• Constructed side length of tridecagon in GeoGebra (display max 15 decimal places) ${\displaystyle a=0.478631328575115\;[unit\;of\;length]}$
• Side length of the tridecagon ${\displaystyle a_{target}=r\cdot 2\cdot \sin \left({\frac {180^{\circ }}{13}}\right)=0.478631328575115534...\;[unit\;of\;length]}$
• 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 in GeoGebra (display max 14 decimal places) ${\displaystyle \mu =27.69230769230769^{\circ }}$
• Central angle of the tridecagon ${\displaystyle \mu _{target}=\left({\frac {360^{\circ }}{13}}\right)=27.{\overline {692307}}^{\circ }}$
• Absolute angular error of the constructed central angle:

Up to the max. displayed 14 decimal places is the absolute error ${\displaystyle F_{\mu }=\mu -\mu _{target}=0.0^{\circ }}$

Example to illustrate the error

At a circumscribed circle radius r = 1 billion km (the light would need about 55 min for this distance), the absolute error of the side length constructed would be < 1 mm.

Licensing

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