File:01-Siebeneck Seite gegeben Animation.gif

Summary[edit]

Description01-Siebeneck Seite gegeben Animation.gif	Deutsch: Siebeneck mit gegebener Seite, Näherungskonstruktion als Animation, am Ende 15 s Pause English: Heptagon with a given side, approximation construction as an animation, at the end 15 s pause
Date	13 March 2016
Source	Own work
Author	Petrus3743
Other versions

Ergebnis[edit]

Bezogen auf eine gegebene Seitenlänge E₁E₂ = 1 [LE][edit]

• Konstruierter Umkreisradius des Siebenecks in GeoGebra (Anzeige signifikante 14 Nachkommastellen) ${\displaystyle R=1{,}15238243548124\;[LE]}$
• Umkreisradius des Siebenecks ${\displaystyle R_{SOLL}={\frac {0{,}5}{\sin \left({\frac {180^{\circ }}{7}}\right)}}=1{,}15238243548124...\;[LE]}$
• Absoluter Fehler des konstruierten Umkreisradius ${\displaystyle F_{R}=R-R_{SOLL}=0{,}0\;[LE]}$
• Konstruierter Zentriwinkel des Siebenecks in GeoGebra (Anzeige signifikante 13 Nachkommastellen) ${\displaystyle \mu =51{,}4285714285715^{\circ }}$
• Zentriwinkel des Siebenecks ${\displaystyle \mu _{SOLL}={\frac {360^{\circ }}{7}}=51{,}4285714285714...^{\circ }}$
• Absoluter Fehler des konstruierten Zentriwinkels nach Anzeige in Geogebra ${\displaystyle F_{\mu }=\mu -\mu _{SOLL}=0^{\circ }}$

Beispiel um den Fehler zu verdeutlichen[edit]

Bei einer Seitenlänge E₁E₂ = 100 Mio. km (das Licht bräuchte für diese Strecke ca. 5,5 min), wäre der absolute Fehler des Umkreisradius < 1 mm.

Result[edit]

Based to a given side E₁E₂ = 1 [unit of length][edit]

• Constructed circumcircle radius of the heptagon in GeoGebra (display significant 14 decimal places) ${\displaystyle R=1.15238243548124\;\;[unit\;of\;length]}$
• Circumcircle radius of the heptagon ${\displaystyle R_{should}={\frac {0.5}{\sin \left({\frac {180^{\circ }}{7}}\right)}}=1.15238243548124...\;[unit\;of\;length]}$
• Absolute error of the constructed circumcircle radius ${\displaystyle F_{R}=R-R_{should}=0{,}0\;[unit\;of\;length]}$
• Constructed central angle of the heptagon in GeoGebra (display significant 13 decimal places) ${\displaystyle \mu =51.4285714285715^{\circ }}$
• Central angle of the heptagon ${\displaystyle \mu _{should}={\frac {360^{\circ }}{7}}=51.4285714285714...^{\circ }}$
• Absolute error of the constructed central (display GeoGebra) ${\displaystyle F_{\mu }=\mu -\mu _{should}=0^{\circ }}$

Example to illustrate the error[edit]

At a side length E₁E₂ = 100 Mio. km, (the light needed for this distance about 5.5 minutes), the absolute error of the circumcircle radius would be < 1 mm.

Licensing[edit]

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