File:01-Angel Trisection.svg
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Summary
[edit]Description01-Angel Trisection.svg |
Deutsch: Dreiteilung des Winkels (exakt) mit Trisektrix-Kurve als zusätzliches Hilfsmittel
English: Angle trisection (exact) with trisectrix curve as additional auxiliary means |
Date | |
Source | Own work |
Author | Petrus3743 |
SVG development InfoField |
Deutsch
[edit]Anwendungsbeispiel
Verwendet ist die bekannte Trisectrix von Colin Maclaurin aus dem Jahr 1742.
Im Kartesischen Koordinatensystem wird diese Kurve beschrieben mit der Gleichung
- ,
durch Umformung ergibt sich die Gleichung für die Implizite Kurve
Dreiteilung eines Winkels
Zuerst wird der Durchmesser mit seinem Mittelpunkt bestimmt. Es folgt der Halbkreis mit der anschließenden Generierung der Trisektrix als Implizite Kurve[1]. Somit ist die Grundkonstruktion für die Dreiteilung von Winkel fertiggestellt. Nun wird der zweite Winkelschenkel so eingezeichnet, dass er mit dem ersten Winkelschenkel den zu teilenden Winkel einschließt. Der Winkelschenkel schneidet die Trisektrix in . Als Nächstes wird ein gerade Linie von durch bis zum Halbkreis gezogen, dabei ergibt sich der Schnittpunkt . Der von und eingeschlossene Winkel ist der gesuchte Winkel .
English
[edit]Application example
The known Trisectrix of Colin Maclaurin from the year 1742 is used.
In Cartesian coordinates this curve is described with the equation
- ,
the equation for the Implicit curve is obtained by transformation
Angle trisection
First, the diameter with its center is determined. This is followed by the semicircle with the subsequent generation of the trisectrix as the implicit curve[1]. Thus, the basic construction for the angle trisection of angles is completed. Now, the second angle limb is drawn in such a way that it encloses with the first angle limb the angle to be divided. The angle limb intersects the trisectrix in . Next, a straight line from is drawn through to the semicircle, resulting in the intersection . The angle generated by and is the angle sought.
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- ↑ a b Dörte Haftendorn: Kurven erkunden und verstehen Kapitel 3.3: S. 62, ISBN 9783658147488, Spektrum, Akademischer Verlag, Springer, 2016, Trisektrix Konstruktion, abgerufen am 12. Januar 2017
File history
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 21:23, 10 January 2017 | 648 × 501 (139 KB) | Petrus3743 (talk | contribs) | Winkelsymbol nachgetragen | |
21:03, 10 January 2017 | 648 × 501 (138 KB) | Petrus3743 (talk | contribs) | M zusätzlich für Mittelpunkt | ||
20:30, 10 January 2017 | 648 × 501 (138 KB) | Petrus3743 (talk | contribs) | Darstellung überarbeitet | ||
17:59, 10 January 2017 | 811 × 626 (126 KB) | Petrus3743 (talk | contribs) | mit Mittelpunkt "a" | ||
16:31, 10 January 2017 | 811 × 626 (126 KB) | Petrus3743 (talk | contribs) | User created page with UploadWizard |
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Width | 18.30036414292473cm |
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Height | 14.142678550525018cm |