Summary

Description01-Achtzehneck-Animation.gif	Deutsch: Achtzehneck, Animation der Näherungskonstruktion English: Octadecagon, animation of the approximate construction
Date	22 October 2015
Source	Own work
Author	Petrus3743
Other versions

Konstruktionsprinzip, Design principle

Näherungskonstruktion

Den Winkel 60° mit vier Winkelhalbierende (w₁ ...w₄) verkleinern und den Kreisbogen MOC zwischen Winkelhabierende w₃ und w₄ mit folgender Näherungslösung dritteln.

Gerade Hilfslinie g visiert über Punkt O den Punkt N an (quasi ein Lineal an die Punkte O und N angelegt), zwischen O und N daher keine Hilfslinie

${\displaystyle {\overline {PQ}}={\frac {1}{3}}{\overline {OP}}}$

Radius ${\displaystyle {\overline {QR}}={\overline {OP}}}$

Proximity construction

Reduce the angle 60° with four angle bisectors (w₁ ... w₄) and thirds the arc between MOC bisector w₃ and w₄ with the following approximate solution.

Straight auxiliary line g aims over the point O to the point N (virtually a ruler at the points O and N applied), between O and N, therefore no auxiliary line

${\displaystyle {\overline {PQ}}={\frac {1}{3}}{\overline {OP}}}$

Radius ${\displaystyle {\overline {QR}}={\overline {OP}}}$

Fehler, Error

Bei einem Umkreisradius r = 1 [LE]:

• Konstruierte Neuneckseite s₁ = 0,347296355243719... [LE]
• Neuneckseite s = 2 • sin(10°) = 0,347296355333861... [LE]
• Absoluter Fehler = s₁ − s = -9,01...E-11 [LE]
  • Bei einem Umkreisradius r = 100 000 km wäre der absolute Fehler der 1. Seite ≈ -9 mm

At a circumscribed circle radius r = 1 [unit of length]:

• Constructed side of nonagon s₁ = 0,347296355243719... [unit of length]
• Side of nonagon s = 2 • sin(10 °) = 0,347296355333861... [unit of length]
• Absolute error = s₁ - s = -9,01... E-11 [unit of length]
  • At a circumscribed circle radius r = 100 000 km would be the absolute error of the 1^st side ≈ -9 mm

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