world population!

http://www.census.gov/main/www/popclock.html

It feels so great to know I am one in 667,04,82,626 !! I feel so great and significant to feel I am one in 667 crores!

Equation in Microsoft Word

I wrote the equation in my post using MS word 2007. It is very very useful. I will recommend it. But has still long way to go.

circumference of an ellipse!

Somehow I never thought about the circumference of an ellipse.

Oh what is there to think about? It is one of the "kid" curves our ancestors figured out, right?Although I am an Indian, most likely my ancestors too - not just Greeks - at any rate it is not as complicated as exponentials and logarithms which form the basis of decimal system - anyone remember having problems with carry in addition in their second standard? [include me as your brethern]

Of course figuring out length of the curve is the most simplest thing taught to me 13-14 years ago at which time of course I sort of cursed myself, that I didn't figure such a simple thing myself - it is just pythogoras thorem

dr^2 = dx^2 + dy^2
and of course I want to find r from dr just integrate over it, so simple ah?
Anyway to come back to main story - Yesterday after reading about classical mechanics and then just to relax I was reading Dawkins' God delusion - [A very good book BTW to give to your religious friends] and somehow my attention turned to earth's orbit and I was thinking why would people think orbit should be circle, especially if it is very improbable configuration among all ellipses. Then I wondered what is the average velocity with which we fly through the space.

It is simply our [earth's] orbit length divided by 365 days! But I didn't know orbit length.

But I knew it is an ellipse - So I wanted to calculate the circumference of the ellipse.
So I duly wrote the equation
x^2/a^2+y^2/b^2=1
and started integrating
sqrt(1+(dy/dx)^2) dx
I didn't even have a hint of what is coming. So I got a nasty expression in terms of x and y s and I thought converting into parameteric form may be easier to solve.
I set x= acos(theta)
...
to cut a long story short
I ended up at

and whatever I do I couldn't solve it. Then today I came and looked on the net [cheating] for circumference of ellipse and sure enough they stop here too and call it 'complete elliptic [obviously] integral of second kind'

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

it has only an infinite series solution and an approximation by Ramanujan!
Sometimes things we take for granted turn out to be so complex!

what the heck is [electron] spin?

This is the kind of thing which drives me nuts in quantum mechanics.
What is this spin with values like h*/2?
electron doesn't rotate on its own axis, right? So what is the meaning of this angular momentum? I know only the I x W
why it behaves like angular momentum if it is not one?
and the misnomer spin totally trips me off.
Really if someone claims he understands QM, what is this thing? [forget uncertainty principle etc.]

principle of least action

Actually principle of extremal action - why should it be true?
Meaning in the ultimate sense - why should universe follow it? not in the sense we can derive newton's 2nd law from this.
what is this thing called action?

I can [sort of] understand energy, force, displacement etc. What is this? It looks like ultimate cooked up thing.

atleast hamiltonian H [in conserved case], I can think of as energy.

But what is this Lagrangian?
[I know QM generalises it to all the paths. So least action is just special case - but still what is it, that it is generalising?]

தமிழ் unicode mapping

தமிழ் எழுத்துகளின் UNICODE எண்கள்!

http://unicode.org/charts/PDF/U0B80.pdf