File:01-257-Eck E-15 Animation.gif

Summary[edit]

Ergebnis[edit]

Bezogen auf den Einheitskreis r = 1 [LE]

• Konstruierte Seite des 257-Ecks in GeoGebra (Anzeige 15 sigifikante Nachkommastellen, gerundet) ${\displaystyle {\overline {E_{257}E_{1}}}=a=2{,}44475829850863E-2\;[LE]}$
• Seite des 257-Ecks, 15 sigifikante Nachkommastellen, ebenfalls gerundet ${\displaystyle a_{SOLL}=2\cdot \sin \left({\frac {180^{\circ }}{257}}\right)=2{,}44475829850863E-2\;[LE]}$

  

• Absoluter Fehler der konstruierten Seite ${\displaystyle F_{a}=a-a_{SOLL}=0\;[LE]}$
• Konstruierter Zentriwinkel in GeoGebra (Anzeige 14 sigifikante Nachkommastellen, gerundet) ${\displaystyle \mu =1{,}40077821011673^{\circ }}$
• Zentriwinkel des 257-Ecks, 14 sigifikante Nachkommastellen, ebenfalls gerundet ${\displaystyle \mu _{SOLL}={\frac {360^{\circ }}{257}}=1{,}40077821011673^{\circ }}$
• Absoluter Fehler des konstruierten Zentriwinkels ${\displaystyle F_{\mu }=\mu -\mu _{SOLL}=0^{\circ }}$

Beispiel um den Fehler zu verdeutlichen[edit]

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

Result[edit]

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

• Constructed side of 257-gon in GeoGebra (Display 15 significant decimal places, rounded) ${\displaystyle {\overline {E_{257}E_{1}}}=a=2.44475829850863E-2\;[LE]}$
• Side of the 257-gon, 15 significant decimals, also rounded ${\displaystyle a_{target}=2\cdot \sin \left({\frac {180^{\circ }}{257}}\right)=2.44475829850863E-2\;[LE]}$
• Absolute error of the constructed side in GeoGebra ${\displaystyle F_{a}=a-a_{target}=0\;[unit\;of\;length]}$
• Constructed central angle in GeoGebra (Display 14 significant decimal places, rounded) ${\displaystyle \mu =1.40077821011673^{\circ }}$
• Central angle of the 257-gon in GeoGebra, 14 significant decimals, also rounded ${\displaystyle \mu _{target}={\frac {360^{\circ }}{257}}=1.40077821011673^{\circ }}$
• Absolute error of the constructed central angle ${\displaystyle F_{\mu }=\mu -\mu _{target}=0^{\circ }}$

Example to illustrate the error[edit]

At a radius r = 1 billion km (the light would need about 55 min for this distance) the absolute error of the first side a would be < 1 mm.

Licensing[edit]

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