Summary edit

Description01 29-Eck-Näherung-E-15.svg	Deutsch: 29-Eck, Näherungskonstruktion English: 29-gon (icosienneagon), approximate construction
Date	22 April 2020
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 Seitenlänge des 29-Ecks in GeoGebra (Anzeige max. 15 Nachkommastellen) ${\displaystyle a=0{,}216238036847884\;[LE]}$
• Seitenlänge des 29-Ecks ${\displaystyle a_{SOLL}=r\cdot 2\cdot \sin \left({\frac {180^{\circ }}{29}}\right)=0{,}216238036847884\ldots \;[LE]}$
• Absoluter Fehler der konstruierten Seitenlänge:

Bis zu den max. angezeigten 15 Nachkommastellen ist der absolute Fehler ${\displaystyle F_{a}=a-a_{SOLL}=0{,}0\;[LE]}$

• Konstruierter Zentriwinkel des 29-Ecks in GeoGebra (Anzeige signifikante 13 Nachkommastellen, gerundet) ${\displaystyle \mu =12{,}4137931034483^{\circ }}$
• Zentriwinkel des 29-Ecks ${\displaystyle \mu _{SOLL}=\left({\frac {360^{\circ }}{29}}\right)=12{,}4137931034483\ldots \;^{\circ }}$
• Absoluter Winkelfehler vom konstruierten Zentriwinkel:

Bis zu den gerundet angezeigten signifikanten 13 Nachkommastellen ist der absoluter Fehler ${\displaystyle F_{\mu }=\mu -\mu _{SOLL}=0^{\circ }}$

Beispiel um den Fehler zu verdeutlichen edit

Bei einem Umkreisradius r = 1 Mrd. km (das Licht bräuchte für diese Strecke ca. 55 min), wäre der absolute Fehler der konstruierten Seitenlänge < 1 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 29-gon in GeoGebra (display max 15 decimal places) ${\displaystyle a=0.216238036847884\;[unit\;of\;length]}$
• Side length of the 29-gon ${\displaystyle a_{target}=r\cdot 2\cdot \sin \left({\frac {180^{\circ }}{29}}\right)=0.216238036847884\ldots \;[unit\;of\;length]}$
• Absolute error of the constructed side length:

Up to the max. displayed 15 decimal places is the absolute error ${\displaystyle F_{a}=a-a_{target}=0.0\;[unit\;of\;length]}$

• Constructed central angle of the 29-gon in GeoGebra (display significant 13 decimal places, rounded) ${\displaystyle \mu =12.4137931034483^{\circ }}$
• Central angle of the 29-gon ${\displaystyle \mu _{target}=\left({\frac {360^{\circ }}{29}}\right)=12.4137931034483\ldots \;^{\circ }}$
• Absolute angular error of the constructed central angle:

Up to the rounded significant 13 decimal places is the absolute error ${\displaystyle F_{\mu }=\mu -\mu _{target}=0^{\circ }}$

Example to illustrate the error edit

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

Licensing edit

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