hey, Lets start some math discussion!

[Tim_Lou]

im trying to prove that
area of circle =pi r^2
and area of ellipse = ab pi
(is it ab pi?)

and i found out something interesting:
that pi =

lim n-->infinity (4/n^2) * (times)

n
sigma [ square root (n^2 - k^2) ]
k=1


is it right? or not?
if it is, any idea to prove it?

(tormod, how can i upload some images??)

[Turtle]

Yes even/odd exists in nature. If I have a pile of 31 beans & you & I wish to fairly share them, we find that using whole beans, no even divison is possible. What is more natural than that.
Further on Fibonacci sequence; in phylotaxy (the numerical arrangement of twigs on a palant) buds appear in a year as a ratio of number of times around the branch over the number of buds. Both numbers are always Fibonacci.
Please visit my site?
http://home.comcast.net/~turtlediable/wsb/index.html

[maddog]

Originally Posted by Freethinker

Perhaps it does. It SEEMS that nature sets things up in "countable" groups. Even wave/ particle collapse seems oriented towards individual elements, not some continous stream. Matter seems to have a finite smallest size. there seems to be a discrete number of electrons/ protons/ ... in an atom and specific measurable quantities of atoms in different molecules, ...

Seems to be in the grouping Fermion/Bosons...

Originally Posted by Freethinker

Or do all these things exist like this because we expect them to? Does the wave collapse into a singular particle because that is what we are measuring for?

This in essence is the Schroedinger's cat thought problem. Quantum entanglement is
here as well.

Originally Posted by Freethinker

Do numbers exist because we want them to? Or did we discover numbers because nature is broken into discrete units?

The Greeks thought numbers were a discovery. Myself, I think of them as an invention to
keep track of all the sheep and goats.

Maddog

[Turtle]

I love math. I have done some work on residues of powers; some graphs under Pictures on my page show this.
http://home.comcast.net/~turtlediable/wsb/index.html