Greatest Equations Ever 1017
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?"
Re:Well... (Score:5, Informative)
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?
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...
Submitter and Parent are stupid (Score:-1, Informative)
Eurler's equations is Exp(i*theta) = cos(theta) + i*sin(theta).
Cos(theta) = -1 for theta being **ODD** multiples of PI radians [not any multiple].
Thus, the equation should be
Exp( (2n+1)*PI ) + 1 = 0, where n is a Natural number (1,2,3,4..).
2n+1 gives us all the odd positive integers...
The parent said Exp(i*PI) +1 = 0, but Exp(2*Pi)= +1, not -1....
--
Please, I need the mod points!
Re:correction (Score:5, Informative)
Guy created so many darn formulae that "Euler's formula" is ambiguous.
Re:Submitter and Parent are stupid (Score:3, Informative)
The only thing is that schematix (grandparent) misread the Pi as a 'n', which look very similar, indeed (on my screen anyway).
Use the (HTML) source, Luke! (Score:2, Informative)
It's OK to use HTML on a website, you know. I suggest:
... which will work nicely in most browsers.
Mine, mine ! (Score:2, Informative)
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.
Re:Actually... (Score:3, Informative)
If it wasn't for the laws of nature things wouldn't work. The mathematical formulas are our way of expressing them.
Mathematical formulas indicate an understanding of such laws, so without that understanding, your cell phone wouldn't work.
Re:Take a guess.... (Score:2, Informative)
If, on the other hand, you choose "simpler" axioms, then you might have to work very hard to get to the point of saying 1 + 1 = 2. Peano's axioms lead very quickly to this--in fact, they are about the same as the ones you stated. But you can assume any set of axioms you want. Much of mathematics is devoted to finding a "minimum set" of axioms for a particular branch, although as Godel showed, mathematics cannot be consistently axiomatic. Alas.
Re:correction (Score:5, Informative)
Talk about throwing the baby out with the bathwater!
Re:V=IR (Score:4, Informative)
What's wrong with AC. R is resistance, not impedance or reactance. If you add reactance to the equasion, then you need a new formula, but that equasion has current, voltage and resistance. The formula holds true. Don't read in inductance and capacatance where there isn't any.
This is Ohm's law, not Kirkoff's law.
For formulas that include reactive components, they are listed here;
http://www.tpub.com/neets/book2/6.htm
and driving the joke into the ground we get .. (Score:3, Informative)
First we state that women require time and money:
Women = Time X Money
error--^
this should be
Women = Time + Money
and from there onwards
And as we all know "time is money"
Time = Money
Therefore by substituting Money for Time we get:
Women = Money + Money
Women = 2(Money)
And because "money is the root of all evil" we therefore can state:
Money = (Evil)^1/2
And Since
2(Money) = Women
and
(Money)^1/2 = Evil
And we are forced to conclude by substituting "women" for "(money)2" from above that:
Women = 2((Evil)^1/2)
or in words
women are double the root of all evil
which means absolutely nothing
but hey when you're a maths nazi..
Suchetha
Re:V=IR (Score:4, Informative)
Re:Einstein's FULL equation (Score:3, Informative)
I sure hope my calculations aren't where all that inexplicable "dark matter energy" has been coming from. . .
Re:Take a guess.... (Score:1, Informative)
Schrödinger! (Score:4, Informative)
H*Psi = E*Psi
(note: H is an operator folks, not a number)
Perhaps not as famous as E=mc^2.. or as exact as the Dirac equation (relativistic version of the S.E.),
but.. in terms of practical benefit to mankind, I think this one has done more than any other equation during the last century.
Atoms. Molecules. Semiconductors. Lasers.
The number of things explained and modelled by the Schrödinger equation are just uncountable. You can explain almost* all of chemistry with that thing.
Relativity is nice, but it hasn't had the technical uses quantum physics has.
(*Relativistic effects are important in heavy elements. For instance the yellow color of gold is a relativistic effect.)
The axioms of set theory (Score:5, Informative)
Re:V=IR (Score:3, Informative)
At any moment in time the equation V=IR holds for any circuit (yes, even AC circuits). It is just that when you have caps and inductors in your AC circuit their impedance changes all the time, making the V=IR equation less usefull.
When one only has resistive impedance elements it is possible to use V=IR for AC circuits by replacing V with Vrms, and I with Irms, the Root-Mean-Square value of the AC voltage or current, giving Vrms = Irms*R.
Re:ThinkGeek t-shirt (Score:2, Informative)
"2+2=5 for extremely large values of 2" is sometimes called "Fermat's next-to-last theorem" and is said to be the occasion for a duel with sabers between Tycho Brahe and Manderup Parsbjerg in 1566.
You can read about the grisly outcome here [straightdope.com] as part of the discussion "Did Tycho Brahe really have a silver nose?".
Re:correction (Score:2, Informative)
What is important is the key fact in its proof, which is that for any value 't', e^it = sin(t) + i*cos(t)
If you have taken calc 1, this should be readable. Think of it this way.
e^it, shows up a lot in engineering formulas, but can be a pain to work with. Being able to convert it to a sin/cosine formula makes it simpler because for certian values of t, sin() or cos() will be 1 or 0, and derivatives and integrals are fairly simple (eg. sin(x) d/dx = cos(x) ).
Slightly old news... (Score:2, Informative)
Re:correction (Score:4, Informative)
-Jesse
Re:correction (Score:3, Informative)
Re:Actually... (Score:4, Informative)
- Albert Einstein, Sidelights on Relativity
Re:correction (Score:3, Informative)
That would be the Euler-Lagrange [wolfram.com] equation.
Re:correction (Score:3, Informative)
Re:Impressions of math equitations. (Score:3, Informative)
In layman's terms, in base 1, 1+1=11, 11+1=111, 111+1=1111, and so on. This is consistent with the requirement that the number of symbols in a number represented in base n contains no more than n distinct symbols. But base 1 contains mathematical inconsistencies when representing non integers (or even the integer 0) which can't permit it to be acceptable as a valid base.
Re:Einstein's FULL equation (Score:1, Informative)
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.
Actually that's not actually what's in there. There's no such a thing as 'mass at rest'... At rest with respect to whose frame of reference???
A more proper terminology and interpretation is that there's a thing we call mass which is the proper mass of an object, or the mass we measure on the frame of reference of the object itself.
The equation, then, tell us that the relation between the energy of a body of mass m and it's momentum is not linear, as thought in Newtonian physics, but it's actually a quadratic wrt the speed of light. WRT a certain frame of reference moving at constant speed from our object, the amount of energy we need to increase its momentum by 1 (units of momentum, Kg*ms^-1 on the IS) is bigger the bigger the object's momentum is.
The mass of an object is a constat, like the speed of light is. Talking of 'rest mass' and all that was caused by eager physicists trying to prove Newton's equations were still valid... But they are not, and telling ourselves lies won't help us understand the Universe better.
BTW, E=mc^2 is the energy of a body of mass m on its own frame of reference; for particles that cannot have a frame reference, like photons and other particles that move at the speed of light, the relation becomes easier, as the massive term dissapears (cannot be mass as there's no proper frame of reference to define it in the first place!) E=pc (which is used a great deal in 1st quantification theories, and helps to find out through DeVroglie's relation the value of Plank's constant h).
So E=pc is as important or even more than E=mc^2...
BTW, the "right" way to write this is, being the tetra-momentum P^mu = (-cm, p), where mu=0,1,2,3; p is a three-dimensiona vector defined as gamma*mv (where gamma is the 1/sqrt(1-v^2/c^2) factor of Lorentz' transformations); ^ means superscript and _ subscript, and the metric tensor M^(mu nu) chosen so that the diagonal elements are time-space= (-1,1,1,1); we get that:
E^2/c^2 = P^mu*M_mu^nu*P_mu = c^2m^2 + p^2
which is the right formula for this case... QED
and if we make c=1 as usual, we get that E^2 = m^2 + p^2; with frontier cases of E=m and E=p, which is easier to read and don't hide the physical meaning of the result...
Umm, electricity has negative. (Score:1, Informative)
Re:correction (Score:2, Informative)
Wow: Try this in Google! (Score:2, Informative)
e^(pi*i)+1 [google.com]
Re:Wow: Try this in Google! (Score:3, Informative)