> No, they are much more difficult to calculate, but they convey more meaning.
Again, I didn't mean approximations like 22/7. I was comparing them to e.g. the geometric method which took hundreds of years to extend to a few hundred digits. The geometric method conveys the same "meaning" because it is an exact description of pi, just like the infinite series and the iterative algorithms.
> Pi isn't just a number, any more than e is.
They are both just numbers. e is not infinite, in fact it is less than 3.
No, they are ideas. The base of natural logarithms isn't an arbitrary number, it has special properties. It's the same with Pi -- they're ideas that happen to be expressible as numbers. But their numerical value is less important than their identity as ideas.
> e is not infinite, in fact it is less than 3.
Straw man. No one claimed otherwise. But e appears to have an infinite digital sequence, i.e. is "normal" in the mathematical sense.
But, as with Pi, the fact that e is likely "normal" is much less important than the idea it represents.
OK. It sounded like you were saying that Pi is special just because there is an infinite series that describes it. It's trivial to make an infinite series that sums to any number. http://en.wikipedia.org/wiki/Series_%28mathematics%29#Conver... So the number 2 is just as "infinite" as pi.
> It sounded like you were saying that Pi is special just because there is an infinite series that describes it.
That would be because Pi is special because there are infinite series, and integrals, and mathematical identities, and limit expressions, that describe it in ways that give it a special meaning.
> So the number 2 is just as "infinite" as pi.
You're confusing the existence of a summation with its outcome. Obviously the sum of 2^-n for n between 0 and infinity (inclusive) is equal to 2, but that doesn't make 2 an infinite digital sequence, or in any other sense "infinite".
Right, those are approximations. Those are not what we are talking about.
> This is valid: https://www.dropbox.com/s/423ieio63bsuaat/pi_w.png
I agree that it is valid. It is one of many ways of calculating the value of pi. Here is another one: http://upload.wikimedia.org/wikipedia/commons/thumb/2/2a/Pi-... Also there are iterative algorithms. http://en.wikipedia.org/wiki/Pi#Computer_era_and_iterative_a...
> No, they are much more difficult to calculate, but they convey more meaning.
Again, I didn't mean approximations like 22/7. I was comparing them to e.g. the geometric method which took hundreds of years to extend to a few hundred digits. The geometric method conveys the same "meaning" because it is an exact description of pi, just like the infinite series and the iterative algorithms.
> Pi isn't just a number, any more than e is.
They are both just numbers. e is not infinite, in fact it is less than 3.