File:01-Siebeneck-E-9 Animation.gif

Summary[edit]

Ergebnis, Score[edit]

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

• Konstruierte Seite des Siebenecks ${\displaystyle s_{k}=0{,}867767469717624...\;[LE]}$
• Seite des Siebenecks ${\displaystyle s=2\cdot \sin \left({\frac {180^{\circ }}{7}}\right)=0{,}867767478235116...\;[LE]}$
• Absoluter Fehler der konstruierten Seite = ${\displaystyle s_{k}-s=-8{,}517...E-9\;[LE]}$
• Relativer Fehler der konstruierten Seite [%] = ${\displaystyle {\frac {s_{k}-s}{s}}\cdot 100\ \%={\frac {0{,}867767469717624-0{,}867767478235116}{0{,}867767478235116}}\cdot 100\ \%=-0{,}00000098\ \%}$
• Konstruierter Zentriwinkel des Siebenecks ${\displaystyle \alpha _{k}=51{,}42857088691416...^{\circ }}$
• Zentriwinkel des Siebenecks ${\displaystyle \alpha ={\frac {360^{\circ }}{7}}=51{,}42857142857142...^{\circ }}$
• Absoluter Fehler des konstruierten Zentriwinkels ${\displaystyle \alpha _{f}=\alpha _{k}-\alpha =-0{,}541...E-7^{\circ }}$

Beispiel um den Fehler zu verdeutlichen[edit]

Bei einem Radius r = 1.000 km wäre der absolute Fehler der 1. Seite ca. -8,5 mm.

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

• Constructed side of the heptagon ${\displaystyle s_{k}=0.867767469717624...\;[unit\;of\;length]}$
• Side of the heptagon ${\displaystyle s=2\cdot \sin \left({\frac {180^{\circ }}{7}}\right)=0.867767478235116...\;[unit\;of\;length]}$
• Absolute error of the constructed side = ${\displaystyle s_{k}-s=-8.517...E-9\;[unit\;of\;length]}$
• Relative error of the constructed side [%] = ${\displaystyle {\frac {s_{k}-s}{s}}\cdot 100\ \%={\frac {0.867767469717624-0.867767478235116}{0.867767478235116}}\cdot 100\ \%=-0.00000098\ \%}$
• Constructed central angle of the heptagon ${\displaystyle \alpha _{k}=51.42857088691416...^{\circ }}$
• Central angle of the heptagon ${\displaystyle \alpha ={\frac {360^{\circ }}{7}}=51.42857142857142...^{\circ }}$
• Absolute error of the constructed central angle ${\displaystyle \alpha _{f}=\alpha _{k}-\alpha =-0.541...E-7^{\circ }}$

Example to illustrate the error[edit]

At a circumscribed circle radius r = 1,000 km, the absolute error of the 1st side would be approximately -8.5 mm.

Licensing[edit]

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

Licensing[edit]

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