File:01-Trisection of angle E-10 Animation.gif
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Size of this preview: 800 × 481 pixels. Other resolutions: 320 × 192 pixels | 640 × 385 pixels | 1,101 × 662 pixels.
Original file (1,101 × 662 pixels, file size: 962 KB, MIME type: image/gif, looped, 81 frames, 3 min 24 s)
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[edit]Description01-Trisection of angle E-10 Animation.gif |
Deutsch: Dreiteilung des Winkels, Näherungskonstruktion als Animation
English: Trisection of an angle, proximity construction as animation |
Date | |
Source | Own work |
Author | Petrus3743 |
Other versions |
Konstruktionsprinzip
[edit]Näherungskonstruktion
[edit]- Den gegebenen Winkel (wenn 180° ≥ ≥ 90°) bzw. den Ergänzungswinkel (wenn 0° < < 90°) mit fünf Winkelhalbierende verkleinern und den Kreisbogen OGH zwischen Winkelhalbierende b4 und b5 mit einer Näherungslösung dritteln.
- Winkelhalbierende: b1 ... b5
- Gerade Hilfslinie g visiert über Punkt H den Punkt G an (quasi ein Lineal an die Punkte H und G angelegt), zwischen H und G keine Hilfslinie, daher frei für Schnittpunkt K.
Fehler
[edit]Bei einem Radius r = OB = 1 [LE]:
- Max. absoluter Fehler des Winkels β ≈ -4E-8°, wenn Winkel α nahezu 0°, bzw. ≈ 4E-8°, wenn Winkel α = 180°.
- Max. absoluter Fehler der Sehne ≈ -6,8E-10, wenn Winkel α nahezu 0°, bzw. ≈ 6,02E-10, wenn Winkel α = 180°.
- Bei einem Radius r = OB = 10.000 km wäre der max. Fehler an der Sehne ≈ -6,8 mm bzw. ≈ 6 mm
Construction principle
[edit]Proximity construction
[edit]- Reduce the given angle (if 180° ≥ ≥ 90°) respectively the complementary angle (if 0° < < 90°) with five angle bisector and the circular arc OGH, between b4 and b5, and thirds him with an approximate solution.
- Angle bisector: b1 ... b5
- Straight auxiliary line g aims over the point H to the point G (virtually a ruler at the points H and G applied), between H and G no auxiliary line, therefore free for intersection K.
Error
[edit]At a circle radius r = OB = 1 [unit of length]:
- Max. absolute error of the angle β ≈ -4E-8° when angle α close to 0°, respectively ≈ 4E-8° when angle α = 180°.
- Max. absolute error on the chord ≈ -6.8E-10, when angle α close to 0°, respectively ≈ 6.02E-10 when angle α = 180°.
- At a radius r = OB = 10,000 km would be the max. error on the chord ≈ -6.8 mm respectively ≈ 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 | 07:28, 13 July 2016 | 1,101 × 662 (962 KB) | Petrus3743 (talk | contribs) | zweites Lineal ergänzt | |
18:03, 12 July 2016 | 1,096 × 640 (949 KB) | Petrus3743 (talk | contribs) | Konstruktion neu | ||
08:31, 9 July 2016 | 1,206 × 742 (1.03 MB) | Petrus3743 (talk | contribs) | Datei neu geladen | ||
22:50, 26 November 2015 | 1,206 × 742 (1.03 MB) | Petrus3743 (talk | contribs) | Überarbeitete Datei | ||
22:31, 26 November 2015 | 1,206 × 742 (1.03 MB) | Petrus3743 (talk | contribs) | aktualisierte Datei hochgeladen | ||
22:23, 26 November 2015 | 1,206 × 742 (1.03 MB) | Petrus3743 (talk | contribs) | Kurzhinweis IJ = IH/3 korr.; "should" korr. | ||
22:58, 1 September 2015 | 1,068 × 666 (881 KB) | Petrus3743 (talk | contribs) | 1 Einheit = 16cm | ||
14:35, 1 September 2015 | 1,202 × 749 (1.04 MB) | Petrus3743 (talk | contribs) | Startbild ergänzt | ||
14:01, 1 September 2015 | 1,202 × 749 (1 MB) | Petrus3743 (talk | contribs) | Vergrößerung des Bildes, 1 Einheit = 18cm | ||
11:20, 1 September 2015 | 1,001 × 624 (821 KB) | Petrus3743 (talk | contribs) | Neukonstruktion |
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