Pi Misconception

 P: 3 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 ?
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P: 26,157
 Quote by Revin Happy Pi day folks !
Happy Pi day to you too! (And welcome to PF!)

(this is a message from the future … it's actually Pi-plus-one day here … are you in Alaska?)
 For example, if the circumfrence is 50.123456 cm ( i've not measured yet just an example) …
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!
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 Quote by Revin For example, if the circumfrence is 50.123456 cm ( i've not measured yet just an example)
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.

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Pi Misconception

 Quote by Revin 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.
You mean why is pi an irrational number. Or why isn't pi a rational 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 ?
No, a "measurement" is never exact. When you talk about "lengths" in geometry you are not talking about measurements.
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 Quote by Mentallic Hypothetically, it should be pi, but realistically, it's impossible to do.
Also unrealistic:
- That the circle's radius is exactly 7 cm.
- That this circle drawn with a compass truly is a circle.
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 Quote by D H Also unrealistic: - That the circle's radius is exactly 7 cm. - That this circle drawn with a compass truly is a circle.
Also
- 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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