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Why can't we square the circle? [Geometry]
posted March 25 2013 21:04.12 by Giorgos Lazaridis

In ancient Greece, people developed geometry and more specifically the Euclidean geometry. The basic characteristic of this geometry was that, one should be able to solve a problem only by using a ruler and a compass, and nothing else!

Squaring the circle means to construct a square that has the same area of a circle of given diameter. To problem is that to do so, the square root of Pi should be constructed fist. In geometry, this is impossible.

[Link: numberphile]

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  • At 6 August 2013, 5:58:20 user Rod wrote:   [reply @ Rod]
    • Constructing a particular scalene triangle first may lead to a solution:

      Geometers easily comprehend that this new concept of Pi (link below) simply complements one ratio (Pi) with another (rPi from the ASR) and both ratios include the same mysterious and stimulating essence of irrationality!

      Because the cosine angle can complement Pi digit-for-digit, this new perspective (allowing the points of a certain scalene triangle to identify a circle's square) illustrates the concept and even promotes intuitive understanding of the Pi ratio.

      This perspective also hints that squaring the circle requires a challenge to irrational numbers - the scalene triangle is a worthy instrument for this challenge: http://www.aitnaru.org/images/Pi_Corral.pdf

      How not to square the circle?
      Believe that it is impossible.

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