Pi miscalculated or not irrational?

[Mr. X]

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?

 

[Muzza]

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)...

 

[arildno]

As Muzza said, Euler proved that pi is irrational.
It was proved to be transcendental by Lindemann in the 19th century, I believe

 

[Muzza]

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.

 

[eJavier]

A really neat demostration of the fact tha Pi is irrational can be found in Spivak's Calculus

 

[arivero]

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?

 

[Muzza]

Yes. (This is just a filler to get rid of the silly "you can't post a message this short"-error).

 

[arivero]

Yes indeed.