File:01-Dreiteilung des Winkels.svg

Summary[edit]

Description01-Dreiteilung des Winkels.svg	Deutsch: Dreiteilung des Winkels, Näherungskonstruktion English: Trisection of an angle, proximity construction
Date	16 January 2015
Source	Own work
Author	Petrus3743
Other versions
SVG development InfoField	The SVG code is valid.   This trigonometry was created with GeoGebra by Petrus3743.   This SVG trigonometry uses the path text method.

Konstruktionsprinzip[edit]

• Näherungskonstruktion
  • Den gegebenen Winkel (wenn 180° ≥ ${\displaystyle \alpha }$ > 90°) bzw. den Ergänzungswinkel (wenn 0° < ${\displaystyle \alpha }$ ≤ 90°) mit vier Winkelhalbierenden verkleinern und den Kreisbogen MFG zwischen Winkelhabierende w₃ und w₄ mit einer Näherungslösung dritteln.

Fehler[edit]

• Max. Winkelfehler von β: δ ≈ ±1,27E-6°, wenn Winkel α nahezu 0° bzw. 180° ist.
• Bei einem Radius r = MA = 100 km wäre somit der max. Fehler an der Sehne ±2,2 mm

Construction principle[edit]

• Proximity construction
  • Reduce the given angle (if 180° ≥ ${\displaystyle \alpha }$ > 90°) or the complementary angle (if 0° < ${\displaystyle \alpha }$ ≤ 90°) with four angle bisector and the circular arc MFG, between w₃ and w₄, and thirds him with an approximate solution.

Error[edit]

• Max. angle error of β: δ ≈ ±1.27E-6°, when angle α is almost 0° or 180°.
• At a radius r = MA = 100 km would thus be the max. error on the chord ±2.2 mm

Licensing[edit]

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https://creativecommons.org/licenses/by-sa/4.0CC BY-SA 4.0 Creative Commons Attribution-Share Alike 4.0 truetrue