File:01-Siebeneck-Animation.gif

Summary[edit]

Description01-Siebeneck-Animation.gif	Deutsch: Siebeneck, Animation der Näherungskonstruktion English: Heptagon, animation of the approximate construction
Date	19 June 2015
Source	Own work
Author	Petrus3743
Other versions

Ergebnis, Result[edit]

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

• Konstruierte Seite des Siebenecks ${\displaystyle s_{k}=0{,}867767268512597...\;[LE]}$
• Seite des Siebenecks ${\displaystyle s=r\cdot 2\cdot \sin \left({\frac {180^{\circ }}{7}}\right)=0{,}867767478235116...\;[LE]}$
• Absoluter Fehler der konstruierten Seite ${\displaystyle F_{sk}=s_{k}-s=-2,097...E-7\;[LE]}$
• Relativer Fehler der konstruierten Seite [%] ${\displaystyle f_{sk}={\frac {s_{k}-s}{s}}\cdot 100\ \%={\frac {0{,}867767268512597-0{,}867767478235116}{0{,}867767478235116}}\cdot 100\ \%=-0{,}000024\ \%}$
• Seite ${\displaystyle ={\overline {AU}}=r\cdot {\frac {4}{3}}{\sqrt {\frac {2\left(43726-1010{\sqrt {105}}+5{\sqrt {1797}}-101{\sqrt {20965}}\right)}{5\left(37471-606{\sqrt {105}}+30{\sqrt {1797}}-101{\sqrt {20965}}\right)}}}\;\approx 0{,}867767268512597\cdot r}$

Beispiel um den Fehler zu verdeutlichen[edit]

Bei einem Radius r = 10 km wäre der absolute Fehler der 1. Seite ca. -2,1 mm.

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

• Constructed side of heptagon ${\displaystyle s_{k}=0.867767268512597...\;[unit\;of\;length]}$
• Side of the heptagon ${\displaystyle s=r\cdot 2\cdot \sin \left({\frac {180^{\circ }}{7}}\right)=0.867767478235116...\;[unit\;of\;length]}$
• Absolute error of the constructed side ${\displaystyle F_{sk}=s_{k}-s=-2.097...E-7\;[unit\;of\;length]}$
• Relative error of the constructed side [%] ${\displaystyle f_{sk}={\frac {s_{k}-s}{s}}\cdot 100\ \%={\frac {0.867767268512597-0.867767478235116}{0.867767478235116}}\cdot 100\ \%=-0.000024\ \%}$
• Side ${\displaystyle ={\overline {AU}}=r\cdot {\frac {4}{3}}{\sqrt {\frac {2\left(43726-1010{\sqrt {105}}+5{\sqrt {1797}}-101{\sqrt {20965}}\right)}{5\left(37471-606{\sqrt {105}}+30{\sqrt {1797}}-101{\sqrt {20965}}\right)}}}\;\approx 0.867767268512597\cdot r}$

Example to illustrate the error[edit]

At a circumscribed circle radius r = 10 km, the absolute error of the 1st side would be approximately -2.1 mm.

Licensing[edit]

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