Summary edit

Description01-Quadratur-des Kreises-9-0-HalberUmfang.svg	Deutsch: Quadratur des Kreises und daraus den halben Kreisumfang (п), Näherungskonstruktion English: Squaring the circle and from this the half circumference (п), proximity construction
Date	14 December 2014
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.

Fehler (Error) edit

Bei einem Kreis mit Radius r = 1 [LE]:

• Konstruierte Seite des Quadrates s = 1,77245384141934376... [LE]
• Soll-Seite des Quadrates s_s = ${\displaystyle {\sqrt {\pi }}\cdot 1[LE]}$ = 1,772453850905516... [LE]
• Absoluter Fehler = s - s_s = -0,000000009486172... = -9,486...E-9 [LE]
• Fläche des konstruierten Quadrates A = s² = 3,141592619962188... [FE]
• Soll-Fläche des Quadrates A_s = ${\displaystyle {\pi }\cdot 1[FE]}$ = 3,141592653589793... [FE]
• Absoluter Fehler = A - A_s = -0,000000033627605... = -3,3627...E-8 [FE]
• Fazit: Sieben Nachkommastellen sind gleich denen von ${\displaystyle {\sqrt {\pi }}}$ bzw. sind gleich denen von ${\displaystyle \pi }$.
  • Bei einem Kreis mit dem Radius r = 1000 km wäre der Fehler der Seite s ≈ -9,5 mm
  • Bei einem Kreis mit dem Radius r = 10 m wäre der Fehler der Fläche A ≈ -3,4 mm²
  • Bei einem Kreis mit dem Radius r = 100 km wäre der Fehler des halben Kreisumfanges U/2 ≈ -3,4 mm

In a circle of radius r = 1 [unit length, ul]:

• Constructed side of the square s = 1,77245384141934376... [ul]
• Target side of the square s_s = ${\displaystyle {\sqrt {\pi }}\cdot 1[ul]}$ = 1,772453850905516... [ul]
• Absolute error = s - s_s = -0,000000009486172... = -9,486...E-9 [ul]
• Surface of the constructed square A = s² = 3,141592619962188... [unit area, ua]
• Target area of the square A_s = ${\displaystyle {\pi }\cdot 1[ua]}$ = 3,141592653589793... [ua]
• Absolute error = A - A_s = -0,000000033627605... = -3,3627...E-8 [ua]
• Conclusion: seven decimal places are equal to those of ${\displaystyle {\sqrt {\pi }}}$ respectively equal to those of ${\displaystyle \pi }$.
  • In a circle of radius r = 1000 km would be the fault of the page s ≈ -9.5 mm
  • In the case of a circle with the radius r = 10 m would be the error of the surface A ≈ -3.4 mm²
  • In a circle of radius r = 100 km, the error of the half circumference would U/2 ≈ -3.4 mm

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