Pi Day Misconception: Is Pi an Irrational Number?

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In summary, the conversation discusses the misconception about being able to measure pi using a compass and a thread. It highlights the impossibility of achieving an exact rational number and the unrealistic aspects of this exercise.
  • #1
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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  • #2
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:
 
  • #3
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.
 
  • #4
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.
 
  • #5
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.
 
  • #6
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.
 

FAQ: Pi Day Misconception: Is Pi an Irrational Number?

What is Pi Day?

Pi Day is an annual celebration of the mathematical constant π (pi). It is observed on March 14th (3/14) because the first three digits of pi are 3.14.

What is an irrational number?

An irrational number is a number that cannot be expressed as a simple fraction or ratio of two integers. This means that the decimal representation of an irrational number never ends and never repeats in a pattern.

Is Pi an irrational number?

Yes, pi is an irrational number. In fact, it is one of the most well-known irrational numbers. Its decimal representation extends infinitely without repeating, making it impossible to express as a fraction.

Why is Pi considered an irrational number?

Pi is considered an irrational number because it cannot be written as a fraction or ratio of two integers. Its decimal representation is infinite and non-repeating, making it impossible to express as a finite or repeating decimal.

Why is it a misconception that Pi is a rational number?

It is a misconception that pi is a rational number because many people assume that all numbers can be expressed as integers or fractions. However, pi is one of many examples of numbers that cannot be expressed in this way. Its irrationality was proven by the ancient Greek mathematician, Euclid, in the 3rd century BC.

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