What is Pi?

[Cawchy87]

I have asked my math teachers this question in the past and they never understood my question. Is there a simple equation that gives us pi? Why is pi so important to us mathmaticaly? Why is it more important than another non-repeating decimal, say Square root 5?

 

[BrAcKeTmAn]

PI = 3.141

it is a multiplication used to find the circumfrence of a circle by timesing the diameter of the circle by PI.

for example if there is a big circle feild that mesures 100 metres accross to you would times it by PI (3.141) and it would tell you that it is 341 metres around the boundry.

 

[Witling]

Pi actually goes on for as many decimal places as you care to go. It is the number that expresses the relationship between the length of a radius and the circumfrence of a circle. Reportedly the ancient Egyptians settled on the square root of 10, 3.16, as being close enough for government work. I have no idea if this is actually true. I do know that pi is calculated by a means other than measuring the length of the radius and the circumference of a circle. Perhaps someone more knowledgeable will elaborate.

 

[zetter]

There are many formulae you can use to calculate pi. Some of them are listed on this site.

I've always used Leibnitz's Formula, PI/4 = 1/1 - 1/3 + 1/5 - 1/7 + ...

 

[bendixG15]

This has to be a put on.........

 

[Cawchy87]

Nope, just looking for the history behind PI and how it came to be. The way it is taught in schools it is just a random never ending number that solves many equations and we have no idea where it came from or why it is used. (I am in high school)

 

[Cogman]

Well, no it is not a random number, I did actually come from somewhere. PI, as I remember correctly, was origionally used to calculate the parimeter around a wheel. The diameter is easy to get, but when measuring around a circle they found that the distance was always equal to the diameter times the constant known as PI. However, because of the nature of perfect circles (no straight lines) the constant PI would have a non repeating infinit decimal.

PI is a wonderful tool, But, IMO, Not quite as wonderful as the constant e..... However it does beat out the constant i (im not an electrical engineer)

 

[Ryoga]

Pi is the ratio between the circumference and the diameter of a circle. As it turns out, this value is constant.

Pi = c / d

 

[jhu]

what if we lived in a universe where pi was different number?

 

[Jeff7]

Originally posted by: jhu
what if we lived in a universe where pi was different number?

We'd have pi equaling 100.3423, and we'd be asking "what if we lived in a universe where pi was a different number?"

Laws of physics and geometry would have to be radically different.

 

[Cawchy87]

Originally posted by: Ryoga
Pi is the ratio between the circumference and the diameter of a circle. As it turns out, this value is constant.

Pi = c / d

Thank you! That answers my question exactly!

 

[NichowA]

More interesting to me than asking what if pi were a different number is why is pi what it already is? Such an impossible number to represent such a simple relationship.

People who think about stuff like this should check out the movie enttitled Pi, it is really quite interesting (don't expect it to be ultra-heavy on mathematics though)

 

[Ryoga]

It's God's way of fscking with you.

 

[Cogman]

, Ive got a good one, After browsing the internet for a couple of minuets.

Pi is

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92225352959101734140733488476100556401824239219269506208

 

[eLiu]

Originally posted by: Ryoga
It's God's way of fscking with you.

No...God's way of fvckign with us is more like e.

 

[Tiamat]

Originally posted by: Cogman
, Ive got a good one, After browsing the internet for a couple of minuets.

Pi is

3.14159265358979323...

I was going to copy and paste the 32 million digits that my computer calculated through Super PI, but you more or less beat me to that

 

[Kyteland]

http://en.wikipedia.org/wiki/Pi

 

[Cogman]

Tiamat, yah, I did calculate pi with one of those programs, but when I found the text file with 125mil digits of pi, I decided that would be easier. (p,s, that is not 1 mil digits, anyways I dont think it is, I did not do the whole file. Too big for me.

 

[Apologiliac]

That is only part of pi, cogman

 

[Cogman]

lol, well, its closer then is needed for any aplication on earth

 

[Vee]

Originally posted by: NichowA
More interesting to me than asking what if pi were a different number is why is pi what it already is? Such an impossible number to represent such a simple relationship.

?

It's not an "impossible" number in any way. It's 'real' number.
It is not a 'rational' number, though. Rational numbers are numbers which can be represented by a relation P/Q, where P and Q are whole signed numbers, integers.
'Rational' numbers, of course, include all finite decimal numbers, since Q can be 10, 100, 1000...
'Rational' numbers, again of course, also include nonfinite decimal sequences, like 1/3 = 0.33333....
'Real' numbers include all 'rational' numbers, but in fact, most 'real' numbers are not 'rational'!
If N is the amount of real numbers and K is the amount of rational numbers, then the relation N/K is infinite!
So you see, - pi is not a rare case at all. On the contrary, numbers like pi, e, 2^½ are the vast majority.

We use the symbols of pi, e, etc, in order to be able to represent some important non rational real numbers *exactly*. If we used approximations for these numbers, in mathematic expressions and equations, errors would creep in.

 

[Topher]

I'll never forget the 3rd Rock episode where John Lithgow stands up and cheers at a football game:

"Pi, Pi, that's our sign
3-point-1-4-1-5-9"

 

[DrPizza]

Also, to answer your question "why is it so important mathematically", part of the answer to that is that Pi creeps into problems, sometimes where you would never expect it. Also, if you want an exact answer and are dealing with trig or circles, or problems dealing with cycles, Pi is frequently part of the answer as well.

 

[Mday]

pi is considered an irrational number. That is, it is not a rational number. A rational number by definition is any number that can be represented as a fraction with WHOLE numbers in the numerator and denominator (none zero for the den.).

Furthermore, it is important that pi and e are "transcendental numbers". That is, they are not algebraic. There is no regular polynomial which will yield pi and e as a root. The only way you can get pi and e, in terms not defined by C/d, is calculus. And, yes, irrational numbers CAN be algebraic, such as the square root of 2, or even 2i.

 

[sao123]

I wonder...
How many other "important" transcendental numbers are out there that we havent discovered?

I've always thought were probably only 1 transcendental number away from having some real scientific breakthrough, like warp fields or time travel.