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square the circle (third-person singular simple present squares the circle, present participle squaring the circle, simple past and past participle squared the circle)

  1. (geometry) To construct a square with the same area as a given circle by using only a finite number of steps with compass and straightedge.
    • 1946, Bertrand Russell, History of Western Philosophy, I.24:
      The problem of squaring the circle is the problem of determining the ratio of the circumference of a circle to the diameter, which is called π.
  2. To solve a famously difficult or impossible problem.


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