What's your favorite equation? (Page 2)

I haven't done the math since grad school, but use QM quite often as implemented in molecular dynamics software. It's funny how some people can grasp math when it's used, but struggle in the abstract. I'm one of them. Got terrible grades in Algebra, Calc, etc. but aced Physics, Physical Biochemistry, etc.

? = :-) (4/3)πtc^iπ

explanation found here

This has stuck with me since high school chemistry since it's silly to "say" as "piv-nert".

I don't know astrophysics and general field theory well enough to get all the jokes but I got a bit of it.  Fun stuff.  It is on Stanfield's official page at SLAC so I would guess it was dated 4/1 of some year.

TW

"m v squared over two g" always sounds poetic to me for some reason.

F=G m1m2/r2.

I always liked all formulas for motion/force/energy/friction.  Physics/statics/dynamic stuff.

They have a wonderful symmetry and poetry.  

Under action of a constant force the motion proceeds along a path that increases the distance folded against itself.

To each according to its mass and in inverse measure of its proximity each to the other at the same time.

In Archimedes' and Aristotle's time, equations were written in natural language without symbols of todays expressions.  Algebraic notation was not invented until the late Renaissance. The advance of science was thus aided by the underlying artistry and poetry in the physics.

TW

I was gonna vote for that one!  (e^i*pi+1=0)

Also a fan of infinite equations --     1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + ... = 2.   

Work = Fd

F = ma

a = g (force of gravity)

Work = mgd.

mgd = beer. (miller genuine draft) 

Work = Beer.

C₆H₁₂O₆    ====>   2(CH₃CH₂OH) + 2(CO₂) 

I just used the Riemann Zeta in a derivation to evaluate an infinite series that came up in an equation for bending. I had never heard of it before. Where else does it show up?

TW

Cheers! (raises glass)

TW

Originally posted by gsmacleod Hard to choose but I've always enjoyed the simple elegance and profound implications of: Shane

At the speeds I personally go, this one is irrelevant.

Originally posted by gsmacleod

Originally posted by tech_geezer

Originally posted by gsmacleod Hard to choose but I've always enjoyed the simple elegance and profound implications of: Shane

At the speeds I personally go, this one is irrelevant.

More time training, less time posting about favourite equations That is certainly part of the elegance of the Lorentz factor for me; how something so insignificant at classical speeds can have such profound consequences as one approaches the speed of light. I've also always enjoyed: Shane

What I remember about learning the wave equation was the amazing use of what seemed to be an artificial, purely mathematical construct of imaginary numbers to represent fundamental real physics.  When you think about it, all numbers, math, and formulas are abstractions of the real thing.  That we can make the association between the abstract thing and the real thing is the amazing part.

Anybody here deal with sorting algorithms?  Here's a cool video of some sorting algorithms visualized
http://www.youtube.com/watch?v=kPRA0W1kECg

I didn't know about the "Cocktail Shaker sort" until that video, but it definitely seems interesting.

I miss math and science terribly.

The first is a favorite (but not the favorite) because it always got the best of me. I can still write some insane equations from memory (and I, too, took QM and advanced biochemistry), but I was never able to remember that goshdarned junior high level equation! It is very lovely, though.

The second, to me, represents everything that is both challenging and awe-inspiring about (un)reality at the quantum level.

(Equations.jpg)

Eigenvectors always kicked my rear when I took Linear Algebra.  Every time I saw one I thought "well there's -5 for this test...".

I'm not certain about that second one.

TW

The power of linear algebra is being able to write out systems of equations with algebraic rules that are much like scalar algebra.  The analogy between scalar and matrix math allows problems to be solved by familiar techniques. The difficulty with this particular equation is that it has no counterpart in scalar algebra.  I use this one a lot to get to the connections between states in state space systems.  It is certainly worth the effort to push through on this one and see where it goes in linear system dynamics.  There are many, many analogous equations in functional analysis too.  The level of abstraction just gets deeper. 

TW