File:01-23-Näherung E-15-Animation.gif

Summary[edit]

Ergebnis[edit]

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

• Konstruierte Seitenlänge des 23-Ecks in GeoGebra (Anzeige max. 15 Nachkommastellen) ${\displaystyle a=0{,}272333298192493\;[LE]}$
• Seitenlänge des 23-Ecks ${\displaystyle a_{SOLL}=2\cdot \sin \left({\frac {180^{\circ }}{23}}\right)=0{,}272333298192493\ldots \;[LE]}$
• 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 23-Ecks in GeoGebra (Anzeige signifikante 13 Nachkommastellen, gerundet) ${\displaystyle \mu =15{,}6521739130435^{\circ }}$
• Zentriwinkel des 23-Ecks ${\displaystyle \mu _{SOLL}={\frac {360^{\circ }}{23}}=15{,}652173913043478\ldots ^{\circ }}$
• Absoluter Fehler des konstruierten Zentriwinkels

Bis zu den gerundet 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 23-gon in GeoGebra (Display max 15 decimal places) ${\displaystyle a=0.272333298192493\;[unit\;of\;length]}$
• Side lenght of the 23-gon ${\displaystyle a_{should}=2\cdot \sin \left({\frac {180^{\circ }}{23}}\right)=0.272333298192493\ldots \;[unit\;of\;length]}$
• 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 23-gon in GeoGebra (display significant 13 decimal places, rounded) ${\displaystyle \mu =15.6521739130435^{\circ }}$
• Central angle of the 23-gon ${\displaystyle \mu _{should}={\frac {360^{\circ }}{23}}=15.65217391304347\ldots ^{\circ }}$
• Absolute error of the constructed central angle

Up to the rounded 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 55 minutes), the absolute error of the 1st side would be < 1 mm.

Licensing[edit]

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