Pi miscalculated or not irrational?

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    Irrational Pi
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The discussion centers on the nature of pi, specifically its classification as an irrational number. It is confirmed that pi is irrational, with historical proofs dating back to the 18th century, including contributions from Lambert and Euler. The conversation addresses the misconception that the imperfection of real-world circles could imply a miscalculation of pi, clarifying that the algorithms used to compute pi do not rely on physical measurements of circles. Additionally, pi is noted to be transcendental, further distinguishing it from algebraic numbers. The conversation emphasizes the established mathematical understanding of pi's properties.
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pi miscalculated or not irrational?

I know that computers have calculated thousands of digits of pi, but does this mean that pi is an irrational number? How can we be so sure that it is irrational? And I have one more question. The circles we see in real life are not perfect circles. Does this mean that pi might have been miscalculated? :confused: :confused: :confused:
 
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I know that computers have calculated thousands of digits of pi, but does this mean that pi is an irrational number?

No, we can calculate thousands of digits of the decimal expansion of 1/3, but that doesn't make it irrational ;)

How can we be so sure that it is irrational?

Because it was proven (way back in 1768, if my googling is correct). See http://www.mcs.csuhayward.edu/~malek/Mathlinks/Pi.html page for a proof.

The circles we see in real life are not perfect circles. Does this mean that pi might have been miscalculated?

No, why would it mean that? I /seriously/ doubt that any of the algorithms used for calculating millions of digits of pi include any measurements of "real" circles...

You might find this page interesting. As you can see, most of those formulas are quite far removed from anything concerning circles (other than the fact that they involve pi, of course)...
 
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As Muzza said, Euler proved that pi is irrational.
It was proved to be transcendental by Lindemann in the 19th century, I believe
 
As Muzza said, Euler proved that pi is irrational.

I didn't say that... ;) Mathworld says that it was Lambert who proved it.

It appears as if the date I gave in my last post was wrong.
 
A really neat demostration of the fact tha Pi is irrational can be found in Spivak's Calculus
 
arildno said:
As Muzza said, Euler proved that pi is irrational.
It was proved to be transcendental by Lindemann in the 19th century, I believe

to be trascendental is the same thing that to be not algebraic, isn't it?
 
Yes. (This is just a filler to get rid of the silly "you can't post a message this short"-error).
 
Yes indeed.
 

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