Summary

Ergebnis

Bezogen auf den Einheitskreis r = 1 [LE]

• Konstruierte Seite des Neunzehnecks GeoGebra ${\displaystyle a=0{,}329189180561468...\;[LE]}$
• Seite des Neunzehnecks ${\displaystyle a_{SOLL}=2\cdot \sin \left({\frac {180^{\circ }}{19}}\right)=0{,}329189180561467788...\;[LE]}$
• Absoluter Fehler der konstruierten Seitenlänge ${\displaystyle F_{a}=a-a_{SOLL}=2{,}12...E-16\;[LE]}$
• Konstruierter Zentriwinkel des Neunzehnecks in GeoGebra ${\displaystyle \mu =18{,}94736842105263...^{\circ }}$
• Zentriwinkel des Neunzehnecks ${\displaystyle \mu _{SOLL}={\frac {360^{\circ }}{19}}=18{,}947368421052631578...^{\circ }}$
• Absoluter Fehler des konstruierten Zentriwinkels ${\displaystyle F_{\mu }=\mu -\mu _{SOLL}=-1{,}578...E-15^{\circ }}$

Beispiel um den Fehler zu verdeutlichen

Bei einem Radius r = 1 Mrd. km (das Licht bräuchte für diese Strecke ca. 55 min) wäre der absolute Fehler der konstruierten Seitenlänge ca. 0,21 mm.

Score

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

• Constructed side lenght of the enneadecagon in GeoGebra ${\displaystyle a=0.329189180561468...\;[unit\;of\;length]}$
• Side lenght of the enneadecagon ${\displaystyle a_{target}=2\cdot \sin \left({\frac {180^{\circ }}{19}}\right)=0.329189180561467788...\;[unit\;of\;length]}$
• Absolute error of the constructed side lenght ${\displaystyle F_{a}=a-a_{target}=2.12...E-16\;[unit\;of\;length]}$
• Constructed central angle of the enneadecagon in GeoGebra ${\displaystyle \mu =18.94736842105263...^{\circ }}$
• Central angle of the enneadecagon ${\displaystyle \mu _{target}={\frac {360^{\circ }}{19}}=18.947368421052631578...^{\circ }}$
• Absolute error of the constructed central angle ${\displaystyle F_{\mu }=\mu -\mu _{target}=-1.578...E-15^{\circ }}$

Example to illustrate the error

At a 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 approx. 0.21 mm.

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