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Greatest Equations Ever
Posted by
timothy
on Mon Oct 25, 2004 04:21 AM
from the comic-shop-guy's-revenge dept.
from the comic-shop-guy's-revenge dept.
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?"
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correction (Score:5, Insightful)
Re:correction (Score:5, Insightful)
Parent
Re:correction (Score:5, Informative)
Guy created so many darn formulae that "Euler's formula" is ambiguous.
Parent
Re:correction (Score:5, Interesting)
...Which is in turn not to be confused with Euler's equation, which is V+F=E+2.
Euler has a ridiculous amount of stuff named after him.
Parent
Re:correction (Score:5, Funny)
A hockey team in Edmonton, Alberta...
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Re:correction (Score:5, Funny)
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Re:correction (Score:5, Funny)
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Re:correction (Score:5, Informative)
It's also got the other important mathematical concepts - exponentiation (i.e. raising something to the power of something else), multiplication, addition and equals. Essentially, it's a huge nugget of maths in a tidy little wrapper.
I've got an old Sharp graphics calculator, which has both proper notation layout and a complex numbers mode. I still like keying in the 'e^(pi*i)+1', pressing 'Enter', then getting the zero, all perfectly laid out on a little LCD display...
Parent
Re:correction (Score:5, Funny)
Oh well. 5318008.
Parent
Joke Time (Score:5, Funny)
Bush opened the letter and it appeared to contain a coded message:
370HSSV-0773H
Bush was baffled, so he typed it out and e-mailed it to Colin Powell. Colin and his aides had no clue either so they sent it to the CIA. No one could solve it, so it went to the NSA and then to MIT and NASA and the Secret Service.
Eventually they asked Britain's M I6 for help. They cabled the White House: "Tell the President he is looking at the message upside down."
Parent
Re:correction (Score:5, Funny)
Oh well. 5318008.
Wouldn't it more appropriate to be: 55378008
Parent
Actually... (Score:4, Insightful)
If it wasn't for the laws of nature things wouldn't work. The mathematical formulas are our way of expressing them.
Parent
Re:Actually... (Score:5, Insightful)
It is a mathematical relationship which is completely abstract - none of those values are physical quantities, although all of them are used in other physical equations.
In theory an alien in a completely different universe could come up with the same formula.
Think about it - e is related to the integral of 1/x on a flat plane - which doesn't exist in real life. i is the square root of -1, which is about as abstract a concept as you'll ever come up with - it certainly doesn't correspond to any physical quantity (unless you define a physical system using complex coordinates for the sake of convenience). Pi is a number which is very useful in practical measurements, but which can be described completely in the abstract.
In any case, an equation like Euler's formula reflects our understanding of mathematics in general more than it reflects our knowledge of any particular physical process.
Parent
Re:Actually... (Score:5, Interesting)
Quantum mechanical wavefunctions are complex. You could define them as two real wavefunctions and work out the appropriate algebra, but it's exactly complex algebra. So i could correspond to the phase difference of two wavefunctions, which would be observable via interference effects.
Not disagreeing with what you're saying though -- the equation is fundamental mathematics, independent of the physical universe, it doesn't make sense to imagine an "alternative universe" where it doesn't apply.
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Re:Actually... (Score:5, Funny)
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Re:Actually... (Score:5, Funny)
=Smidge=
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Re:Actually... (Score:5, Funny)
Parent
Re:correction (Score:5, Informative)
Talk about throwing the baby out with the bathwater!
Parent
sum of cubes (Score:5, Interesting)
first proof, that i'd seen at least, of the existance of negative numbers.
Re:sum of cubes (Score:5, Funny)
Parent
Re:sum of cubes (Score:5, Interesting)
I say, that until I saw the sum of cubes I internally denied the existance of negative numbers. I mean I could work with them and all, I just didn't believe in them. If you deny the existance of negative numbers, you cannot have an expression 0-1, because -1 is meaningless, so therefor the result is meaningless. It's circular reasoning, and this is why[according to my youthful very non-standard way of thinking of things]:
there is a number -1
there is a number 0
if you have two numbers, there is a third number which represents their sum.
there is a number -1 + 0
if there is a number -1 + 0 there must be a class of numbers known as negative numbers
[the direction you were going in?]
but if you cannot prove there is a number -1 + 0, you cannot even get that far.
a^3+b^3 = (a+b)(a^2 - ab + b^2 ), on the other hand, shows quite clearly that no matter what numbers a and b you pick, you end up, in your equation, with a negative number.
Parent
V=IR (Score:5, Interesting)
Re:V=IR (Score:5, Interesting)
twinkle twinkle little star
power equals I squared R
I remembered it.
Parent
Re:V=IR (Score:5, Funny)
There was once a football player who was teetering on the edge of academic eligibility. To help the poor guy with his physics test, the coach told him:
Remember this ryme, to get the power in a circuit:
Twinkle twinkle little star,
Power equals I squared R.
Well the school day before the exam, the football player also had a big game. He tackled alot of people and had a really good day. However, the next day he failed his test! The coach couldn't understand, so he asked the player if he remembered the ryme. The football player said:
Of course, coach:
Twinkle twinkle star in the sky,
Power equals R squared I!
There's a moral in there somewhere. :-)
Parent
Take a guess.... (Score:5, Funny)
Take a look at the username, and take a guess at mine :o)
Re:Take a guess.... (Score:5, Funny)
But shurely 1
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Re:Take a guess.... (Score:5, Interesting)
http://mathworld.wolfram.com/Logic.html [wolfram.com]
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Geometry and Algebra (Score:5, Interesting)
Well... (Score:5, Funny)
B*u*pi * integral of e^x
Hint: Try writing it in mathematical notation.
Re:Well... (Score:5, Informative)
Parent
Re:Well... (Score:5, Funny)
Yay!
Parent
H = F ^ 3 (Score:4, Insightful)
From Woz.
It's the most important and beautiful equation I've ever seen.
ThinkGeek t-shirt (Score:5, Funny)
It is not just funny... if you consider the numbers not as integers, but as any float value with that integer as the first number, it is true.
Dirac's equation of 1/2 spin: (Score:5, Interesting)
Said by Hotson to be the Equation of Everything. First part [zeitlin.net], second part [zeitlin.net]. Worth a read IMO.
0 = 0 (Score:5, Funny)
dupe of old poll (Score:5, Informative)
Shashdot has already covered this in a poll! We all already know that E=mc^2 is the overall favorite, closely followed by F=ma.
http://slashdot.org/pollBooth.pl?qid=804 [slashdot.org]
Einstein's FULL equation (Score:4, Informative)
Anyway, just thought I'd share that because E=m^2c^4 + p^2c^2 is my favorite equation and most people think it looks a little familiar but wouldn't know what it was without a little additional explanation.
Re:Einstein's FULL equation (Score:5, Informative)
Nah?
Parent
Re:Einstein's FULL equation (Score:5, Informative)
It's actually E^2 = (m^2 * c^4) + (p^2 * c^2)
More like: E^2 = (m0^2 * c^4) + (p^2 * c^2)
m0 is defined as the mass at rest (v = 0). If you substitute m = m0 / sqrt(1 - v^2/c^2), you can rework that to E = mc^2. And, if v = 0, you get E0 = m0c^2, the "energy at rest" of an object.
I agree with the original poster, the full version is much more useful than the E = mc^2 form. The short form hides one of the most important conclusions of relativity theory: that mass is a function of speed.
Parent
(Generalized) Stokes equation (Score:5, Insightful)
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.
Everything = 42 (Score:4, Funny)
Everything = 42
One my calc teacher showed me (Score:5, Funny)
Sin x / n = 6
The logic of this was that the n on the bottom cancelled out the n on the top so the result was Six. Oh well I laughed when I was shown it.
1+1=10 (Score:5, Funny)
There are 10 kinds of people: those who understand binary and those who don't.
The Slashdot Equation (Score:5, Funny)
garbage in = garbage out
Jolyon
The importance of notation (Score:5, Interesting)
Apropos to the current discussion was this response [mathforum.org]:
Gotta be a winner: (Score:5, Funny)
Of course if sets aren't your thing...
At the moment... generalized Fourier series (Score:5, Interesting)
Simple stuff, but incredibly cool, considering that Fourier series don't always have to involve just sines and cosines, and you get similar sorts of behaviour.
The axioms of set theory (Score:5, Informative)
Another.. (Score:5, Interesting)
Z = z^2 + c
^^ This simple equation is the generator of Mandelbrot (and Julia) set, arguably the richest fractal known to us..
Re:Impressions of math equitations. (Score:5, Funny)
Those who understand binary
Those that don't
And those that think they do.
Parent