Pi Day Misconception: Is Pi an Irrational Number?

[Revin]

Happy Pi day folks !
Heres a general misconception I am 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 isn't pi an irrational number. After all I am 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 ?

 

[tiny-tim]

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!

 

[Mentallic]

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.

 

[HallsofIvy]

Happy Pi day folks !
Heres a general misconception I am 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 isn't pi an irrational number.

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

After all I am 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.

 

[D H]

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.

 

[Mentallic]

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.