File:01-Neuneck-mit-gegebener-Seite.svg
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Summary
editDescription01-Neuneck-mit-gegebener-Seite.svg |
Deutsch: Neuneck (Nonagon) bei gegebener Seitenlänge, Näherungskonstruktion
English: Nonagon at a given side length, approximate construction |
Date | |
Source | Own work |
Author | Petrus3743 |
Other versions |
![]() Nonagon, animation of the approximate construction ![]() Nonagon, at a given side length, animation of the approximate construction |
SVG development InfoField |
Konstruktionsprinzip
editNäherungskonstruktion
edit- 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
edit- Es ist eine Konstruktion bei gegebenem Umkreis oder bei gegebener Seitenlänge darstellbar.
Fehler
editBei 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
editProximity construction
edit- 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
edit- It is a construction at a given circumscribed circle or at a given side length displayed.
Error
editAt 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
editI, the copyright holder of this work, hereby publish it under the following license:
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This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 21:11, 23 August 2016 | ![]() | 969 × 871 (94 KB) | Petrus3743 (talk | contribs) | User created page with UploadWizard |
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Width | 27.347197879292814cm |
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Height | 24.577861385187212cm |