File:01- Dreiteilung des Winkels 60°.svg
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Summary
[edit]Description01- Dreiteilung des Winkels 60°.svg |
Deutsch: Dreiteilung des Winkels 60°, Näherungskonstruktion English: Trisection of the angle 60°, Proximity construction |
Date | |
Source | Own work |
Author | Petrus3743 |
Other versions | |
SVG development InfoField |
Konstruktionsprinzip
[edit]Näherungskonstruktion
[edit]- Winkel = 60°
- Analog zu File: 01-Dreiteilung des Winkels, wegen der geringeren Schrittanzahl unterscheiden sich die Bezeichnungen der Punkte!
- Beginnt der Kreisbogen b um den Punkt M ab dem Punkt E und endet im Punkt B, ist der Punkt G auf der Hilfslinie g gut erkennbar. Somit kann bereits ein Winkel 60° direkt gedrittelt werden.
- Den Winkel 60° mit vier Winkelhalbierenden verkleinern und den Kreisbogen MED zwischen Winkelhabierende w3 und w4 mit einer Näherungslösung dritteln.
- Winkelhalbierende: w1 ...w4
- Gerade Hilfslinie g visiert über Punkt E den Punkt D an (quasi ein Lineal an die Punkte E und D angelegt), zwischen E und D daher keine Hilfslinie
- Radius
Zusätzliche Approximationen herleitbar
[edit]- Neuneckseite
- Seite vom 36-Eck, Näherungskonstruktion Winkel 10°
- Näherungskonstruktion Winkel 5°
Fehler
[edit]- Die Fehler der Winkel β bzw. γ sind zu gering für eine korrekte Anzeige in GeoGebra, sie werden deshalb als exakt 20° bzw. 40° angezeigt.
- Neuneckseite: Bei einem Radius r = MA = 100.000 km wäre der Fehler an der Sehne ca. 8,6 mm.
Construction principle
[edit]Proximity construction
[edit]- Angle = 60°
- Analog to file: 01-Dreiteilung des Winkels, because of the lower number of steps are different the designations of the points!
- Begins the circular arc b to the point M from the point E and ends at point B, is the point G over the guide g easily recognizable. Thus, already an angle 60° be divided into three directly.
- Do downsize the angle 60° with four angle bisectors and make a thirds of circular arc MED with an approximate solution between angle bisectors w3 and w4.
- Angle bisector: w1 ...w4
- Straight auxiliary line g aims over the point E to the point D (virtually a ruler at the points E and D applied), between E and D, therefore no auxiliary line
- Radius
Additional approximations derivable
[edit]- Side of nonagon
- Side from 36-gon, approximate construction angle 10 °
- Approximate construction angle 5 °
Error
[edit]- The errors of the angles β and γ are too low to correct display in GeoGebra, they will therefore displayed as exactly 20 ° or 40 °.
- Side of nonagon: At a radius r = MA = 100,000 km the error to the chord would be about 8.6 mm.
Licensing
[edit]I, the copyright holder of this work, hereby publish it under the following license:
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.
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 12:07, 19 September 2015 | 805 × 745 (317 KB) | Petrus3743 (talk | contribs) | nicht transparent | |
12:00, 19 September 2015 | 805 × 745 (317 KB) | Petrus3743 (talk | contribs) | Bezeichnung für Bogen b | ||
14:35, 12 June 2015 | 804 × 737 (313 KB) | Petrus3743 (talk | contribs) | Grafikfehler korrigiert | ||
14:24, 12 June 2015 | 786 × 736 (315 KB) | Petrus3743 (talk | contribs) | neue Konstruktion | ||
22:45, 11 June 2015 | 1,183 × 1,108 (345 KB) | Petrus3743 (talk | contribs) | Kreisbogen b gekürzt | ||
11:46, 2 May 2015 | 1,183 × 1,108 (343 KB) | Petrus3743 (talk | contribs) | Typografie "Side" | ||
11:41, 2 May 2015 | 1,183 × 1,108 (344 KB) | Petrus3743 (talk | contribs) | Komma gesetzt | ||
11:30, 2 May 2015 | 1,177 × 1,100 (341 KB) | Petrus3743 (talk | contribs) | Teile vom Text gelöscht, Eintragungen in Englisch ergänzt | ||
14:29, 24 February 2015 | 1,019 × 1,006 (443 KB) | Petrus3743 (talk | contribs) | Gerade in Hilfslinie geändert | ||
09:10, 20 February 2015 | 1,019 × 1,006 (442 KB) | Petrus3743 (talk | contribs) | im Text Gerade g ohne Index |
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Height | 21.03104827699786cm |