5

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?

Pradeep Suny
  • 1,603

2 Answers2

2

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.

https://en.wikipedia.org/wiki/Squaring_the_circle

Ethan Bolker
  • 95,224
  • 7
  • 108
  • 199
1

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

Will Jagy
  • 139,541
  • 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. – Pradeep Suny Nov 16 '19 at 15:53
  • @PradeepSuny That's nice. If you wish to learn something, see http://zakuski.math.utsa.edu/~jagy/papers/Intelligencer_1995.pdf – Will Jagy Nov 16 '19 at 15:58