Pi

[Monoc]

Originally Posted by chardish

1:1.619 is the golden proportion, I thought.

It's better known as the golden ratio. As others said, it's common in nature as well as useful when doing recusive functions.

The golden ratio relationship of a rectangle is neat. If you have a rectangle with the golden ratio, than if you remove the largest square possible from your rectangle, the remaining shape will be a rectangle with the golden ratio.

[TheEndisNear]

maybe pi has a deeper meaning than just being a number... maybe it holds something deep within its numbers... like the meaning of life... ok maybe not but still, it's a thought

It's just the freaking ratio of a circle's circumference to its diameter. I can't stand trying to find deeper meaning in pi.

[makaveli121212]

its tasty

[GuidoHunter]

Man, I can't believe nobody's posted the way to calculate pi yet.

This is gonna be hard without some equation program, but I'll try anyway.

::Searches through Cal II notes::

okay, begin with the function:
f(x)=1/(1+x^2)
and its power series representation:
[Sum; n goes fromzero to infinity] of (-1)^n*x^(2n)

if you integrate the first, you get :
F(x)=arctan(x)
if you integrate the second, you get:
[Sum; n goes fromzero to infinity] of (-1)^n (x^(2n+1)/(2n+1)

Since we're staying in the radius of convergence, we can legally say that arctan(x) equals the second power series, with a constant of integration tacked on (which turns out to be zero if you put x=0 into both sides).

Therefore, when we expand the series (by plugging in values of n, incremented by integers, and adding all the terms) and show the first few terms, we get this:

arctan(x) = x - (x^3)/3 + (x^5)/5 - (x^7)/7 + (x^9)/9 - ...

That ellipsis (the three periods denoting continual addition FOREVER) is important because it shows that you can add terms FOREVER, however small, only getting closer to the real value. From here it's easy to find a representation for pi. Just plug in 1 for x. atan(x)=pi/2, so we plug in:

pi/2 = 1 - 1/3 + 1/5 - 1/7 + 1/9 - ...

Multiply both sides by two, and voila, there's our method of calculating pi.

pi = 2 - 2/3 + 2/5 - 2/7 + 2/9 - ...

There is no end to pi. It doesn't repeat because you're constantly adding different terms.

Q.E.D.? It's a proof....

Oh, and the golden ratio isn't represented by phi, but rather psi. And it's awesome, too, because it's found in nature, because nature is fractal in many places.

--Guido

http://andy.mikee385.com/

[deposition]

damn, didnt think it would be that complicated...although i guess i get the gist of it

[peregrine]

one of my highschool math teachers told a story of 3 mathematicians (grandfather-father-son relation) who dedicated their lives to finding more digits to Pi in the... 1500-1600's? I think. Anyways, the story goes that the 3rd one found out that his grandfather had made a mistake VERY early on in the calculation, hence, their result, and lives, were pretty much useless.

That's gotta suck.

dunno how true that is, but it was relevant in an amusing way.

[Omeganitros]

While we're at it, anyone read Life of Pi? Great book.

[nickadeemus]

What would happen if our way of doing math was completely different. We had a differen't form of calculating amounts, used different "number" values, just happened to come up with a different way to look at things. Just what's been going through my head as I read this.

[Ice-Dragon]

That's the great thing about math. Most of it is not open to different interpretations, it is based on a set of proven rules/theorys. Even if we used different "number values", in essence it would still be the same.

Ex. 2X + 3Y = 0

Let a = the conversion factor between our old numbers and new numbers, assuming we had different "number values"

Becomes ---> 2aX + 3aY = 0
which is equivalent to ---> 2X + 3Y = 0

Most parts of math are definite; so no matter how we looked at it we would still come up with the same theories/rules.

[Nightstar]

nah, we use base 10 math, i think he means if we used like base 5, or did math in roman numerals, or like the egyptians

[Ice-Dragon]

Well yeah it would look different but what I was trying to say was... even if we used some kind of different form like perhaps base 5 or roman numerals, if there were a way of somehow converting the rules and theories developed under that system into base 10, they would appear the exact same.

For example, the relation between the radius of a circle and the circumference of a circle will always remain the same. It is simply a property of a circle. No matter what number system it is written in, the relation between those two things will never change.

[alainbryden]

Originally Posted by deposition

damn, didnt think it would be that complicated...although i guess i get the gest of it

gist.

bored.[/b]

[Thingy]

phi is one "h" of a lot cooler than pi
pi is just A ratio.
phi is THE ratio.

but i do think that e is the coolest and most important of them all.
Just think of what we wouldnt have if we didnt have ln or e^x.

[deposition]

gist.

raddle raddle thunder cladder boom boom bam! dont worry see the car x man!!

[talisman]

there are other functions that are their own derivatives than just e^x.

I think pretty much everything in the form of ae^x will work, where a is a nonzero constant.

[deposition]

Wish i would have paid a little bit more attention when physics teacher was talking about derivitives.

[alainbryden]

physics? try gr. 11 calculus.

[deposition]

He tought us about derivitives in physics...
and uhh its grade 11 physics normally for my school
and our school teaches pre-calc at grade 11.

[AasumDude]

Originally Posted by chillywilly

Pi is a circe. Is that not important enough?

pi is not a circle. Pi is the rato of a circle's circumfrence to its diameter. and i only know 3.2425926535897932384626433832795028841971