File:01-Achtzehneck-Animation.gif
Summary
| Description |
Deutsch: Achtzehneck, Animation der Näherungskonstruktion English: Octadecagon, animation of the approximate construction |
| Date | |
| Source | Own work |
| Author | Petrus3743 |
| Other versions |
 Octadecagon, approximate construction |
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
- Radius
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
- Radius
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 1st side ≈ -9 mm
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