File:01-Siebeneck Seite gegeben.svg

Summary[edit]

Description01-Siebeneck Seite gegeben.svg	Deutsch: Siebeneck mit gegebener Seitenlänge, Näherungskonstruktion English: Heptagon with a given side length, approximation construction
Date	20 May 2018
Source	Own work
Author	Petrus3743
SVG development InfoField	The SVG code is valid.   This trigonometry was created with GeoGebra by Petrus3743.   This SVG trigonometry uses the path text method.

Näherungsonstruktion[edit]

• Die Methode ähnelt der des Dreizehnecks

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.

Approximate construction[edit]

• The method is similar to that of the Tridecagon

Result[edit]

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

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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