If we take a rope of length $x$ which is rational quantity and we make a circle out of it, we measure its diameter which is also rational, if we divide a rational number by another rational number we should get a rational number but the division of length of circumference and diameter should give $π$ which is irrational...?


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  • $\begingroup$ When you do that you get an approximate of $\pi$ not the actual value of $\pi$. $\endgroup$ – The Integrator May 7 '18 at 15:25
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    $\begingroup$ "we measure its diameter which is also rational" : you measure a rationa approximation of the diameter. $\endgroup$ – Mauro ALLEGRANZA May 7 '18 at 15:25
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    $\begingroup$ If the circumference is rational then the diameter is not. $\endgroup$ – Michael Hardy May 7 '18 at 15:25
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    $\begingroup$ We know the $\pi$ is irrational because we prove it be so, not because we have measured it. The distinction between mathematics and land surveying was discovered by Ancient Greeks. $\endgroup$ – Mauro ALLEGRANZA May 7 '18 at 15:27
  • $\begingroup$ Not sure why this is getting downvoted. So you can only ask questions here if you know enough math to not need to ask them, huh? $\endgroup$ – Jack M May 7 '18 at 16:19

When you measure the length of something or the diameter of a circle in real life it looks like some rational number ... but that doesn't mean it is. In real life you just can't get any precise measurement of something.

And don't forget that math is an abstraction ... Lines in math have no thickness, whereas ropes in real life do; so how exactly would you even measure the diameter when laying the rope in a circle?


The diameter will not be rational. It will be a rational number divided by $\pi$.

  • $\begingroup$ Or approximately so, anyway; remembering that we're talking about the diameter of a rope circle the measurement is not going to be very exact. $\endgroup$ – Graham Kemp May 7 '18 at 15:32
  • $\begingroup$ This seems to be the only answer OP needs. Talking about the distinction between a measurement and the true value of something just seems like it might confuse them. $\endgroup$ – Jack M May 7 '18 at 16:20

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