I don't know if there is any way to geometrically construct a circle with a given length of circumference.

I have tried several options but don't seem to get it. Any construction I think of, involves π, which I think is impossible to construct geometrically, right?

Any help?

  • 1
    $\begingroup$ "Ruler" is the wrong word here. Otherwise the answer is "use your ruler to find the length $1/2\pi$... "Straightedge" is probably what you mean. $\endgroup$ – B. Goddard Nov 16 at 15:35
  • $\begingroup$ @B.Goddard, thank you, I edited the title. $\endgroup$ – Pradeep Suny Nov 16 at 15:39

This construction is equivalent to squaring the circle, so there is no such construction:

In 1882, the task was proven to be impossible, as a consequence of the Lindemann–Weierstrass theorem which proves that $\pi$ is a transcendental, rather than an algebraic irrational number; that is, it is not the root of any polynomial with rational coefficients.



cannot be done. $\pi$ is not just irrational, it is transcendental.

  • $\begingroup$ My friends who gave me the problem claim that it can be constructed because we don't need to calculate the exact value of the radius; just to construct it. $\endgroup$ – Pradeep Suny Nov 16 at 15:53
  • $\begingroup$ @PradeepSuny That's nice. If you wish to learn something, see zakuski.math.utsa.edu/~jagy/papers/Intelligencer_1995.pdf $\endgroup$ – Will Jagy Nov 16 at 15:58

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