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?"

correction

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.

Re:correction

Actually, isn't Euler's formula Exp[i*theta] = cos[theta] + i*sin[theta] ? and then substitute in the value of pi into theta, and the more famous result appears.

Re:correction

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.

Re:correction

...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.

Re:correction

Euler has a ridiculous amount of stuff named after him.

A hockey team in Edmonton, Alberta...

Re:correction

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...

Re:correction

Too bad my mathematical abilities don't reach beyond spelling rude words on calculators held upside-down.

Oh well. 5318008.

sum of cubes

a^3+b^3 = (a+b)(a^2-ab+b^2)
first proof, that i'd seen at least, of the existance of negative numbers.

Re:sum of cubes

I mean, you're right it does. But man, was I skeptical.

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.

V=IR

Gotta Love V=IR. Works pretty well, I use it daily, well that and P=VI.

Take a guess....

Some of the equations mentioned were the simplistic 1+1=2 and Euler's equation, e^in + 1 = 0. What are some of your favorite equations?"

Take a look at the username, and take a guess at mine :o)

Re:Take a guess....

Take a look at the username, and take a guess at mine :o)

But shurely 1 /\ 1 = 1 ? [wikipedia.org]

Geometry and Algebra

In my opinion, the most important equations are those that brought together Algebric representation of Geometry -- that has been the single most fundamental basis for today's advancement in mathematics and physics.

Well...

I'm quite fond of this one...

B*u*pi * integral of e^x

Hint: Try writing it in mathematical notation.

Re:Well...

thats buttsex for those of you who dont know how to write an integral

Re:Well...

Slashdot - the only place where you could stay ontopic and mention buttsex and integral in the same sentence _and_ get modded informative.

Yay!

ThinkGeek t-shirt

My favorite is the thinkgeek tshirt that says "2+2=5 for extremely large values of 2".

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:

ih/2Pi dPhi/dt = hc/2iPi (A1 dPhi/dx1 + A2 dPhi/dx2 + A3 dPhi/dx3) + A4 mc(squared)Phi

Said by Hotson to be the Equation of Everything. First part [zeitlin.net], second part [zeitlin.net]. Worth a read IMO.

0 = 0

My favorite is 0 = 0, because it's the one that most often indicates you're done with the math exercise. :-)

dupe of old poll

"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 [slashdot.org]

(Generalized) Stokes equation

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.

One my calc teacher showed me

I always liked this one that my calc teacher says he saw once on a students paper
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

There are 10 kinds of people: those who understand binary and those who don't.

Re:Einstein's FULL equation

I think your favorite equation should be E^2=m^2c^4+p^2c^2.
Nah?

Re:Impressions of math equitations.

There are 11 types of people:
Those who understand binary
Those that don't
And those that think they do.