File:01-Quadratur-des Kreises-9-0-wiki.svg

Summary[edit]

Description01-Quadratur-des Kreises-9-0-wiki.svg	Deutsch: Quadratur des Kreises English: Squaring the circle
Date	23 October 2014, 19:25:45
Source	Own work
Author	Petrus3743
SVG development InfoField	The SVG code is valid.   This trigonometry was created with GeoGebra by Petrus3743.   This SVG trigonometry uses the path text method.

Konstruierte Seite des Quadrates[edit]

${\displaystyle s=2r\cdot {\sqrt {{\frac {25}{36}}+\left({\frac {1}{6}}+{\frac {348+5{\sqrt {143}}}{36\left(72+{\sqrt {143}}\right)}}\right)^{2}}}\;\approx 1{,}77245384141934376\cdot r}$

Fehler[edit]

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

• Konstruierte Seite des Quadrates s = 1,77245384141934376...[LE]
• Soll-Seite des Quadrates s_s = ${\displaystyle {\sqrt {\pi }}}$ = 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 = ${\displaystyle {\pi }}$ = 3,141592653589793... [FE]
• Absoluter Fehler = A - A_s = -0,000000033627605... = -3,3627...E-8 [FE]
• Fazit: Sieben Nachkommastellen 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

Licensing[edit]

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