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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?"
thats buttsex for those of you who dont know how to write an integral
"What is your favorite equation? ..."
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
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.
When things get complex, multiply by the complex conjugate.
It combines the 5 most important numbers in all of mathematics into a single formula.
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...
Tedious Bloggy Stuff - hooray?
There's a difference between "Euler's formula" and "Euler's Formula", depending on whether you're referring to one of his formulae or the specific formula called "Euler's Formula".
Guy created so many darn formulae that "Euler's formula" is ambiguous.
No, everybody is correct.
The only thing is that schematix (grandparent) misread the Pi as a 'n', which look very similar, indeed (on my screen anyway).
It's OK to use HTML on a website, you know. I suggest:
... which will work nicely in most browsers.
I have discovered a truly remarkable
my stupid one would be : lim( sqrt(8) , 8->9) = 3 :)
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.
Mathematical formulas indicate an understanding of such laws, so without that understanding, your cell phone wouldn't work.
RTFM; please, I beg you.
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.
To follow knowledge like a sinking star, / Beyond the utmost bound of human thought. ("Ulysses", Tennyson)
It was my mistake in the original posting. Not the article from Physics world, as I couldn't put in special characters.
Talk about throwing the baby out with the bathwater!
"Leo Fender was in a 'state of grace' when he designed the Stratocaster." -- Paul Reed Smith
Obviously another person who never uses AC.
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
The truth shall set you free!
you've made an error in your initial assumption, which gives a wrong answer
..
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
learn from yesterday, plan for tomorrow, party tonight
or one out of three ain't bad
You're making a big mistake- you're assuming R has to be a constant. It doesn't need to be. R is the resistance, which can be a formula. Actually, it is a formula- R=l*psi/A where l is length, A is cross sectional area, and psi is the resistivity of the substance (which again, can be a formula that takes in temperature, or may be a constant for given material and temperature).
I still have more fans than freaks. WTF is wrong with you people?
To be precise, which is always a virtue in issues of math: It's at proposition 110.643 on page 83 of the second volume of Principia.
Come on, folks? The Schrödinger equation!
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 answer is simple. The most beautiful equations, hands down, are those from which all of mathematics can be derived. These are the axioms of ZFC set theory. What could possibly be more beautiful or more important than that? And it's a shame so few people know about them. See Zermelo-Fraenkel Axioms and Metamath Proof Explorer.
Obviously another person who never uses AC
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.
# ssh -l neo the_matrix; killall -9 agent_smith
"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 as part of the discussion "Did Tycho Brahe really have a silver nose?".
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) ).
Remember, You are unique...just like everyone else.
This news story was in The Times about a month ago... I can recall it interviweing some of the people that voted for 1 + 1 = 2 as the best equation. Euler's was probably the best of them. In itself it seems to show the beauty and... strangeness of math in that three entirely irrational numbers that you'd feel have no link whatsoever can be so intristically linked.
that is Pi up there, not n. It's a very small font, so it may look like an n, but it's actually a PI symbol...
-Jesse
Nothing says "unprofessional job" like wrinkles in your duct tape.
Actually, it's not named after Euler, just by him. He did pick the name for the constant, but only picked 'e' because a, b, c, and d were already common elsewhere.
- Albert Einstein, Sidelights on Relativity
Great minds think alike; fools seldom differ.
That would be the Euler-Lagrange equation.
qntm.org
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.
File under 'M' for 'Manic ranting'
Negative numbers exist in nature, in electricity.
Actually, according to the wikipedia, Euler was not the first person to discover this, but rather, Roger Cotes. Though the wikipedia says he proved it in an obscured form. Search for "Euler's formula" in the wikipedia to confirm.
In theory, theory and practice are the same; in practice they're different. (Yogi Berra & A. Einstein)
Who needs a calculator anymore? Google cannot be stopped:
e^(pi*i)+1