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Pi Misconception

  1. Mar 15, 2014 #1
    Happy Pi day folks !
    Heres a general misconception im having. It might turn out to be a pretty easy question so please do help me.

    If i pull out my compass to a radius of 7 cm and draw a circle on a paper. Then i'll take a piece of thread and cut it such that it matches exactly with the circle on paper and take the length of that particular thread and divide by 14cm, should i get the value of pi ?

    If its so, why isnt pi an irrational number. After all im dividing the circumfrence i've got by 14 cm.
    So it should a rational number.

    For example, if the circumfrence is 50.123456 cm ( i've not measured yet just an example)
    And i divide it by 14cm

    I shall get 50123456/14000000 as value of pi, which is supposedly rational ?

    Is it an contradiction ? :eek:
  2. jcsd
  3. Mar 15, 2014 #2


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    Happy Pi day to you too! (And welcome to PF!) :smile:

    (this is a message from the future … it's actually Pi-plus-one day here … are you in Alaska?)
    But your measurement won't be an exact rational number, will it?

    No matter to how many decimal places you try to measure it, you'll always find a little left over! :wink:
  4. Mar 15, 2014 #3


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    How would you manage to measure it to such precision? There are many reasons why an irrational number like pi will be approximated to a rational number with real world measurements. Hypothetically, it should be pi, but realistically, it's impossible to do.
  5. Mar 15, 2014 #4


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    You mean why is pi an irrational number. Or why isn't pi a rational number.

    No, a "measurement" is never exact. When you talk about "lengths" in geometry you are not talking about measurements.
  6. Mar 15, 2014 #5

    D H

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    Also unrealistic:
    - That the circle's radius is exactly 7 cm.
    - That this circle drawn with a compass truly is a circle.
  7. Mar 15, 2014 #6


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    - The thread perfectly tracing the circle.
    - The thread perfectly maintaining that same length after being stretched out straight.
    - The ruler being perfect.

    Even the thread's physical properties are limiting the perfectness of this imperfect exercise.
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