Pi Misconception

  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. tiny-tim

    tiny-tim 26,016
    Science Advisor
    Homework Helper

    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. Mentallic

    Mentallic 3,783
    Homework Helper

    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. HallsofIvy

    HallsofIvy 41,264
    Staff Emeritus
    Science Advisor

    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. D H

    Staff: Mentor

    Also unrealistic:
    - That the circle's radius is exactly 7 cm.
    - That this circle drawn with a compass truly is a circle.
  7. Mentallic

    Mentallic 3,783
    Homework Helper

    - 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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