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Greatest Equations Ever
sgant writes "What is your favorite equation? This was the question asked by Physics World in a recent poll. This is also covered in a New York Times article about the same poll. Some of the equations mentioned were the simplistic 1+1=2 and Euler's equation, ei + 1 = 0. What are some of your favorite equations?"
Euler's equation is actually Exp[i*Pi] + 1 = 0 not Exp[i*n] +1 = 0 (unless they say n = Pi, which they don't). I'd have to say this is the most elegant equation of all time. It combines the 5 most important numbers in all of mathematics into a single formula. This formula also has tremendous applications in many fields of engineering and other areas of applied mathematics. If it wasn't for this equation, your cell phone wouldn't work.
Scott
Happiness = Food x Friends x Fun
From Woz.
It's the most important and beautiful equation I've ever seen.
The integral of a differential form on the boundry of a manifold is equal to the integral of the exterior derivative on the manifold itself.
S_{dM)w=S_(M)dw
An important special case is the fundamental theorem of calculus. Not only is this a beautiful looking theorem, but important too.
Other special cases are the classical forms of green's theorem, stoke's theorem, and the divergence theorem.
I dunno if its my favorite equation, but its up there.
It's actually E^2 = (m^2 * c^4) + (p^2 * c^2), so for objects with no momentum (only rest mass energy) you can sqaure-root both sides and get E = m * c^2
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If it wasn't for this equation, your cell phone wouldn't work.
If it wasn't for the laws of nature things wouldn't work. The mathematical formulas are our way of expressing them.
Really, I know what I'm doing...Ohhhh, look at the shiny buttons!
Another way of writing the equation E=mc^2 is to we write what m is. m = m0 / [1 - v^2/c^2] (Where m0 is the rest mass - i.e. the mass of the particle when it is stationary - relativity states that the mass of a particle changes when its velocity increases - f=ma is only a newtonian approximation). Therefore, E = m0 c^2 / [1 - v^2/c^2}
Murphy's Law of Research: Enough research will tend to support your theory.
0.999999... is just another way of symbolising the value 1. Its the same value, just two ways to write it.
this is not my signature.
I use this in day-to-day life probably more than anything else. Helpful for calculating my home theater projector screen sizes when I need to one-up friedns that get new televisions.
>although as Godel showed, mathematics cannot be consistently axiomatic. Alas. Mathematics *is* consistently axiomati[zable|c]. It's just not complete.
A classic misquote. The verse actually runs, "The love of money is the root of all evil," but this joke wouldn't be as funny that way.
It's still funny--you just have to change the punchline to "The love of money is the root of all women."
What part of "shall not be infringed" is so hard to understand?
of these, i would say that perhaps the most important is the Generalized Stokes Theorem: http://mathworld.wolfram.com/StokesTheorem.html
this says that the integral of a form over the boundary of a manifold is equal to the integral of the exterior derivative of the form over the manifold itself. it shows that the derivative itself implies topological content!
this beautiful equation says everything one needs to know about the calculus of geometry. from this equation one can derive the fundamental theorem of calculus, vector analysis, antisymmetric tensors, metrics, etc.
i may get this thing tatooed on myself.
As a computer scientist, I quickly learned:
1+1=2 (already knew that)
1+1=1 (boolean)
1+1=10 (binary)
1+1=11 (unary)
It looks like you're considering some kind of low-velocity expansion of an equation for the full energy of a particle, which has a (1/sqrt(1-v^2/c^2) in it. So, you're not even giving the "full" equation.
For my part, I was actually amazed that (what is typically called) "the Einstein equation", (TeX notation)
G_{\mu\nu} = 8\pi T_{\mu\nu}
didn't even appear in the article. I mean, if we're talking "greatest equations ever", something that describes the curvature of spacetime AND the motion of objects in it, which uses 10 nonlinear coupled partial differential equations to do it, but can be derived from a variational principle --- hell, yea it's messy, but it's also pretty simple, powerful and maybe even elegant. The fact that it's still keeping researchers busy to even SOLVE the thing 100 years later certainly makes it interesting.
(How come this didn't make the list, but "e^{i\pi}+1 = 0" did? Big deal.)
A^2+B^2=C^2
This is the only equation that will give you the quickest way from here to there in an airplane.
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Yeah, but it ain't easy. -- Simba