Pi

[dgercone2]

pi no end
universe no end

Connection?

[tnyhwk900]

I would like to know how to calculate pi. Just to clear my concience. Yeah.

Anyone know?

[Anonymous]

...AND I know the longest word in the english language: Pneumonoultramicroscopicsilicovolcanoconiosis

damn i thought it was supercalafragalisticexpealadousous

[perfect_fat]

Pneumonoultramicroscopicsilicovolcanoconiosis

I dont know if that's considered english, cuz it's all scientific and such.

The biggest one I know of is.... (deep breath)

antidisestablishmentarianism

[jewpinthethird]

I dont know if this has anything to do with the number itself, but a perfect circle doesnt have a beginning or end really.

Phi (1.618) is cooler than Pi though.

"Pi is exactly 3.14"
-Professor John Frink

Could you explain about Phi a little more

and your quote reminds me of a simpsons episode

"PI IS EXACTLY 3" (it was to get everyones attention at a math conventino)

Phi = 1.618 and is the nature number. All things in nature relate to this number.

Ex. Messure the length of your arm (shoulder to the tip of your middle finger), then divide the length from your elbow to your finger tips. It should come very close. (Read the DiVinci Code for a better explaination).


And the quote is from the Simpsons (but I might have messed it up), but John Frink is the scientific/nerdy guy.

[makaveli121212]

actually it wasnt even a math convention...it was at an science convention when Lisa showed that bullies picked on nerds becasue of the smell of their sweat...her test subject was named Francien...phi comes out of fibonnaci, which is used so often on nature its unbelievable, which makes it much cooler than pi...but i cant get away from e

[VxDx]

n00bs.

π = ln(-1)/i

[User6773]

1:1.619 is the golden proportion, I thought.

And pi isn't fascinating just because it's never-ending. Every math n00b knows that nonrepeating decimals are very common. Take the square root of any number that's not a perfect square, and you've got one.

[alainbryden]

e is also a cool number. The function e^x is the only function whose derivative is itself.

[VxDx]

derivative of 0 is 0, but I suppose 0 isn't really the best example of a "function".

[Monoc]

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]

hmm

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

[User6773]

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/