Expert: Scott A Wilson - 7/20/2009

Question
First of all, I am a layperson, and a pretty ignorant one at that, so pretend I'm a five-year old, and you'll hit me just about right.

I have been reading about the brothers Chudnovsky who are computing pi out past two billion places, with never a pattern to be found, at least discernibly. Question: I was wondering if there was any research being done with pi relating to its presence in more than one dimension?

I was trying to think about how pi could be a regular shape and still not be repetitive, but infinite. The only way I could come up with a plausible idea was if pi is actually a three or four dimensional (or more) spiral or sphere, not a mere two dimensional closed circle. It also occurred to me that pi may in some way be related to gravity.

Again, I'm a perfect nobody and know very little about mathematics, but pi is very interesting to me and I'm just asking what is probably a very silly question that isn't clear at all..

Answer
Dimensions
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pi is used in many dimensions.

1
If pi is being looked at in 1 dimension, it comes up in trig functions when degrees are converted to radians.
A angle of x degrees is converted to radians by
multiplying by pi/180.

2 In terms of areas, the area of a circle is pi*r*r, where r is the radius.  This is the same as pi*r^2, since r^2 = r*r.

3 In terms of volume, pi is used in finding the volume of a sphere.
The volume V is V = 4*pi*r^3/3 ( where r^3 means multiply 3 r's together, or r*r*r).

In other words, pi arises in any dimension and is always the same number.  The reason it is not repeatable is there are several sums that go off to infinity that can be used to find pi.

Article
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A good article to read is http://en.wikipedia.org/wiki/Pi

Description of pi
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It also difines pi just like I did in terms or length and area under the section Definition.

Down in the section titled, Irrationality and transcendence,
there is a proof that pi is irrational.  
That is, irrational means it has no repeating digits - ever.

The paper than has a section on the numerical value of pi to 50 digits and tells how that, with it, you can calculate anything from the size of the universe down to the size of an atom.  It also has articles where it can be found to a greater number of digits.

The next section speaks of calculating pi.

As far as knowing pi, there is a secition called Memorizing Digits.
The longest one has been by a student in China.  It took him 24 hours and four minutes to recite 67,890 digits of pi.  Now I thought that I happened to know a few, but I only know the first 60.

This paper also lists other places it is used, such as when dealing with complex numbers.  A complex number is one that involves the squareroot(-1).  This is commonly referred to as i.
There is another number known as e, that is used as an exponential in banking, physics, and other places.  

What amazes me is that despite the fact that e and pi are irrational and i is complex, e^(i*pi) = -1.

Summary
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The number pi is a complicated number.
The more math you know, the more places it can arise.
The more places that it arises, the more fascinating it becomes.

As an add on, the number e is also a number that arises a lot.

e is 2.71828182845905..., and also goes on without end.

It just fasicnates me that e^(i*pi) = -1.