File:01-Trisection of angle E-10 Animation.gif

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Description
Deutsch: Dreiteilung des Winkels, Näherungskonstruktion als Animation
English: Trisection of an angle, proximity construction as animation
Date
Source Own work
Author Petrus3743
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Dreiteilung des Winkels, Näherungskonstruktion
Trisection of an angle, proximity construction

Konstruktionsprinzip

Näherungskonstruktion

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

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

Proximity construction

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

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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Category:CC-BY-SA-4.0#01-Trisection%20of%20angle%20E-10%20Animation.gifCategory:Self-published work
Category:Non-SVG images by Petrus3743 Category:Geometric constructions Category:Angle trisection Category:Animations of geometry Category:Animations of ruler and compass constructions Category:Animated GIF files between 50 MP and 100 MP Category:Animated GIF files Category:Approximation
Category:Angle trisection Category:Animated GIF files Category:Animated GIF files between 50 MP and 100 MP Category:Animations of geometry Category:Animations of ruler and compass constructions Category:Approximation Category:CC-BY-SA-4.0 Category:Geometric constructions Category:Non-SVG images by Petrus3743 Category:Self-published work