File:01-Neuneck-Animation.gif
Summary
| Description |
Deutsch: Neuneck (Nonagon) bei gegebenem Umkreis, Animation der Näherungskonstruktion English: Nonagon at a given circumscribed circle, animation of the approximate construction |
| Date | |
| Source | Own work |
| Author | Petrus3743 |
| Other versions |
 Nonagon at a given circumscribed circle, approximate construction  Nonagon, at a given side length, animation of the approximate construction |
Konstruktionsprinzip
Näherungskonstruktion
- Den Winkel 60° mit vier Winkelhalbierende (w1 ...w4) verkleinern und den Kreisbogen MON 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
- Radius
Besonderheit
- Es ist eine Konstruktion bei gegebenem Umkreis oder bei gegebener Seitenlänge darstellbar.
Fehler
Bei einem Umkreisradius r = 1 [LE]:
- Konstruierte Neuneckseite s1 = 0,684040286737346... [LE]
- Neuneckseite s = 2 • sin(20°) = 0,684040286651337... [LE]
- Absoluter Fehler = s1 − s = 8,6...E-11 [LE]
- Bei einem Umkreisradius r = 100 000 km wäre der absolute Fehler der 1.Seite ≈ 8,6 mm
Construction principle
Proximity construction
- Reduce the angle 60° with four angle bisectors (w1 ... w4) and thirds the arc between MON 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.
- Radius
Special feature
- It is a construction at a given circumscribed circle or at a given side length displayed.
Error
At a circumscribed circle radius r = 1 [unit of length]:
- Constructed side of nonagon s1 = 0.684040286737346 ... [unit of length]
- Side of nonagon s = 2 • sin(20 °) = 0.684040286651337 ... [unit of length]
- Absolute error = s1 - s = 8,6 ... E-11 [unit of length]
- At a circumscribed circle radius r = 100 000 km would be the absolute error of the 1st side ≈ 8,6 mm
Licensing
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