File:01-Neunzehneck-Animation.gif

• 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 ${\displaystyle F_{\mu }=\mu -\mu _{SOLL}=-1{,}578...E-15^{\circ }}$

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.

• 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 ${\displaystyle F_{\mu }=\mu -\mu _{target}=-1.578...E-15^{\circ }}$

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.

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