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A line segment of length 22/7 units or 3.14 units can be drawn. But how can a line segment be drawn of exactly pi units?

Asit Srivastava
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  • Start with a line segment of $\tau$ units and half it. - Or if you give me a circle of perimeter one and a line segement of unit length, I could construct length $\pi$ as well. -- Or if you allow me certain other tools beyond straight edge and compasses ... – Hagen von Eitzen Jun 05 '18 at 17:41
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    You need to clarify what tools you have available. If you are asking for a construction using straight-edge and compass and a predetermined unit-length, then it is impossible. Of course, if you are given a ruler of length exactly $\pi$, then it is easy to do. – JMoravitz Jun 05 '18 at 17:43
  • Well, if you can roll a circle to make distances you can. But with classical compass/straightedge constructions you can not. – fleablood Jun 05 '18 at 17:44
  • Thank. I meant the classical compass and the straight edge constructions. – Asit Srivastava Jun 05 '18 at 17:45
  • Sorry, I didn't check it. I have joined today itself. Should I delete the question if anything happens like this? – Asit Srivastava Jun 05 '18 at 17:49
  • "Sorry" About what?, "I didn't check it." Check what. "Should I delete the question if anything happens like this?" What? Something like what? You asked a perfectly good question. Why should you delete it? – fleablood Jun 05 '18 at 17:55
  • I meant if the same question has already been asked and missed it by chance. – Asit Srivastava Jun 05 '18 at 17:57
  • "I meant the classical compass and the straight edge constructions. " I figured you probably did. But one needs to be clear. If you have solid cone as a tool you are allowed to make marks on you can do this. And if you can "curl up" a line you can, of course, uncurl a circle (which dismisses the entire difficulty of measuring the length of a curve.) – fleablood Jun 05 '18 at 18:00
  • Oh... You can delete this question if you want. But it's marked as a duplicate. ... But, you didn't do anything wrong. – fleablood Jun 05 '18 at 18:01

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Due to the transcendence of $\pi$ it is impossible to draw a line segment that is exactly $\pi$ long. However, one could get close by breaking a circle with radius $\frac 12$ and drawing length of its circumference (perhaps using string around the circle).

Rhys Hughes
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