File:01-257-Eck-Animation.gif

Summary[edit]

Description01-257-Eck-Animation.gif	Deutsch: Das 257-Eck mit Näherungskonstruktion der ersten Seite als Animation English: The 257-gon with approximate construction of the first side as an animation
Date	6 June 2015
Source	Own work
Author	Petrus3743
Other versions

Ergebnis, Score[edit]

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

• Konstruierte Seite des 257-Ecks ${\displaystyle {\overline {AE_{1}}}=a=2{,}44475843350370...E-2\;[LE]}$
• Seite des 257-Ecks ${\displaystyle a_{SOLL}=2\cdot \sin \left({\frac {180^{\circ }}{257}}\right)=2{,}44475829850863...E-2\;[LE]}$
• Absoluter Fehler der konstruierten Seite ${\displaystyle F_{a}=a-a_{SOLL}=1{,}3499...E-9\;[LE]}$
• Konstruierter Zentriwinkel ${\displaystyle \alpha =1{,}40077828746899...^{\circ }}$
• Zentriwinkel des 257-Ecks ${\displaystyle \alpha _{SOLL}={\frac {360^{\circ }}{257}}=1{,}40077821011673...^{\circ }}$
• Absoluter Winkelfehler vom konstruierten Zentriwinkel ${\displaystyle F_{\alpha }=\alpha -\alpha _{SOLL}=7{,}735...E-8^{\circ }}$

(1 Winkelsekunde = ${\displaystyle {\frac {1^{\circ }}{3600}}}$ = 0,000277...° = 2,77...E-4°)

Beispiel zur Verdeutlichung des Fehlers[edit]

Bei einem Umkreisradius R = 1000 km wären die absoluten Fehler von:

• 1. Seite ≈ 1,35 mm
• 257. Seite ≈ -350 mm

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

• Constructed side of 257-gon ${\displaystyle {\overline {AE_{1}}}=a=2.44475843350370...E-2...\;[unit\;of\;length]}$
• Side of the 257-gon ${\displaystyle a_{SHOULD}=2\cdot \sin \left({\frac {180^{\circ }}{257}}\right)=2.44475829850863...E-2\;[unit\;of\;length]}$
• Absolute error of the constructed side ${\displaystyle F_{a}=a-a_{SOLL}=1.349...E-9\;[unit\;of\;length]}$
• Constructed central angle ${\displaystyle \alpha =1.40077828746899...^{\circ }}$
• Central angle of the 257-gon ${\displaystyle \alpha _{SHOULD}={\frac {360^{\circ }}{257}}=1.40077821011673...^{\circ }}$
• Absolute angular error of the constructed central angle ${\displaystyle F_{\alpha }=\alpha -\alpha _{SOLL}=7.735...E-8^{\circ }}$

(1 arcsecond = ${\displaystyle {\frac {1^{\circ }}{3600}}}$ = 0.000277...° = 2.77...E-4°)

Example to illustrate the error[edit]

At a circumscribed circle R = 1000 km, would be the absolute errors of:

• Side 1st ≈ 1.35 mm
• Side 257th ≈ -350 mm

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