File:Squaring the circle.djvu

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Research article describing an approximate squaring of the circle using ruler and compass (exact squaring is impossible with just those two).

Source Photocopy of reprint of vol. V (1913) of the Journal of the Indian Mathematical Society, page 132, found in "Ramanujan - Collected Papers".
Author Srinivasa Ramanujan
(Reusing this file)

Public domain because author has been deceased for more than 70 years.

Übersetzung in die deutsche Sprache[edit]

Journal der indischen Mathematical Society, v. 1913, S. 132

  1. Ziehe einen Kreis mit PQR um Mittelpunkt O, wovon der Durchmesser PR sei. (Ergänzung: Q noch nicht bestimmt)
  2. Halbiere PO bei H, der Punkt T ist die Dreiteilung von OR nahe R.
  3. Zeichne TQ senkrecht zur PR und die Sehne RS = TQ.
  4. Verbinde P mit S und zeichne die Parallelen TN und OM zu RS.
  5. Lege eine Sehne PK = PM und ziehe die Tangente PL = MN.
  6. Verbinde R mit L, R mit K und K mit L.
  7. Schneide RC = RH.
  8. Zeichne CD parallel zu KL, trifft auf RL bei D.

Dann ist das Quadrat über RD etwa gleich dem Kreis PQR

Für ,

wobei der Durchmesser des Kreises ist.


Da PL und PK gleich sind mit MN und PM

ist somit und

Damit ist


Aber ,


Deshalb dies ist sehr nahe. Ergänzung: Abweichung = 7,52...E-8 [LE]


Wenn die Fläche des Kreises 140.000 Quadratmeilen ist, dann ist RD etwa einen Zoll größer als die wahre Länge.

Ergänzung zur Bemerkung

1 Meile [mile] = 1.609,344 m

mile2 = 374,165738... mile

RD = 1,772453926158302 m



RD2 = 3,14159292035398 (sechs Nachkommastellen sind gleich denen von )

(-) = 3,14159265358979

Abweichnung zu = 2,66764190737234E-7 mm


Public domain

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current14:48, 14 July 2007Thumbnail for version as of 14:48, 14 July 20071,497 × 2,169 (17 KB)GrafZahl (talk | contribs){{Information |Description=Research article describing an approximate squaring of the circle using ruler and compass (exact squaring is impossible with just those two). |Source=Photocopy of reprint of vol. V (1913) of the Journal of the Indian Mathematica
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