Description01-Trisection of an angle E-10.svg	Deutsch: Dreiteilung des Winkels, Näherungskonstruktion English: Trisection of an angle, proximity construction
Date	28 July 2015
Source	Own work
Author	Petrus3743
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SVG development InfoField	The SVG code is valid.   This trigonometry was created with GeoGebra by Petrus3743.   This SVG trigonometry uses the path text method.

Den gegebenen Winkel (wenn 180° ≥ ${\displaystyle \alpha }$ ≥ 90°) bzw. den Ergänzungswinkel (wenn 0° < ${\displaystyle \alpha }$ < 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.

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

Reduce the given angle (if 180° ≥ ${\displaystyle \alpha }$ ≥ 90°) respectively the complementary angle (if 0° < ${\displaystyle \alpha }$ < 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.

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

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