File:01-Vierzehneck-2.svg

Summary[edit]

Description01-Vierzehneck-2.svg	Deutsch: Regelmäßiges Vierzehneck, Näherungskonstruktion English: Regular tetradecagon, approximation construction
Date	29 June 2016
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 den Einheitskreis r = 1 [LE][edit]

• Konstruierte Seitelänge des Vierzehnecks in GeoGebra ${\displaystyle a=0,445041867912629...\;[LE]}$
• Seitelänge des Vierzehnecks ${\displaystyle a_{SOLL}=2\cdot \sin \left({\frac {180^{\circ }}{14}}\right)=0,4450418679126288089...\;[LE]}$
• Absoluter Fehler der konstruierten Seitenlänge ${\displaystyle F_{a}=a-a_{SOLL}=1,911...E-16\;[LE]}$
• Konstruierter Zentriwinkel des Vierzehnecks in GeoGebra ${\displaystyle \mu =25,714285714285705...^{\circ }}$
• Zentriwinkel des Vierzehnecks ${\displaystyle \mu _{SOLL}={\frac {360^{\circ }}{14}}=25,714285714285714285...^{\circ }}$
• Absoluter Fehler des konstruierten Zentriwinkels ${\displaystyle F_{\mu }=\mu -\mu _{SOLL}=-9,285...E-15^{\circ }}$

Beispiel um den Fehler zu verdeutlichen[edit]

Bei einem Radius r = 1 Mrd. km (das Licht bräuchte für diese Strecke ca. 56 min) wäre der absolute Fehler der 1. Seite ca. 0,2 mm.

Approximate construction[edit]

• The method is similar to that of the Tridecagon

Result[edit]

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

• Constructed side length of the tetradecagon in GeoGebra ${\displaystyle a=0.445041867912629...\;[unit\;of\;length]}$
• Side length of the tetradecagon ${\displaystyle a_{target}=2\cdot \sin \left({\frac {180^{\circ }}{14}}\right)=0.4450418679126288089...\;[unit\;of\;length]}$
• Absolute error of the constructed side length ${\displaystyle F_{a}=a-a_{target}=1.911...E-16\;[unit\;of\;length]}$
• Constructed central angle of the tetradecagon in GeoGebra ${\displaystyle \mu =25.714285714285705...^{\circ }}$
• Central angle of the tetradecagon ${\displaystyle \mu _{target}={\frac {360^{\circ }}{14}}=25.714285714285714285...^{\circ }}$
• Absolute error of the constructed central angle ${\displaystyle F_{\mu }=\mu -\mu _{target}=-9.285...E-15^{\circ }}$

Example to illustrate the error[edit]

At a radius r = 1 billion km (the light would need about 56 min for this distance) the absolute error of the side length constructed would be approx. 0.2 mm.

Weblinks[edit]

Vierzehneck u. a. mit Konstruktionsbeschreibung, Tetradecagon with description of the construction (German)

Licensing[edit]

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