Pi Day Misconception: Is Pi an Irrational Number?

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Discussion Overview

The discussion revolves around the nature of pi as an irrational number, prompted by a participant's inquiry about measuring the circumference of a circle and dividing it by the diameter. The scope includes conceptual misunderstandings about measurements, rationality, and the properties of pi.

Discussion Character

  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions whether dividing the measured circumference of a circle by its diameter should yield a rational number, suggesting a contradiction regarding pi's irrationality.
  • Another participant argues that measurements can never be exact, implying that any rational approximation of pi derived from measurements will always have discrepancies.
  • Concerns are raised about the precision of real-world measurements, with participants noting that achieving exact values for circumference and radius is practically impossible.
  • Several participants highlight the limitations of physical measurements, such as the imperfections in drawing a circle with a compass and the properties of the measuring thread.

Areas of Agreement / Disagreement

Participants generally agree that real-world measurements cannot yield exact values, but there is no consensus on the implications for the rationality of pi itself. The discussion remains unresolved regarding the relationship between measurement and the nature of pi.

Contextual Notes

Limitations include the dependence on the precision of measurements, the idealization of geometric constructs, and the inherent imperfections in physical tools used for measurement.

Revin
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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 ? :eek:
 
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Revin said:
Happy Pi day folks !
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?)
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! :wink:
 
Revin said:
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.
 
Revin said:
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 ? :eek:
No, a "measurement" is never exact. When you talk about "lengths" in geometry you are not talking about measurements.
 
Mentallic said:
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.
 
D H said:
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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