Favourite Formula/Theorem
 

I came upon an article on <a href="http://www.guardian.co.uk/life/science/story/0,12996,1320625,00.html">the greatest equations of all time</a>. I was inspired. So, along similar lines as the coolest number thread, what is your favourite formula (from math or science), equation, theorem, etc.?

Mine is the Binomial Theorem.

http://img12.paintedover.com/uploads...ialtheorem.gif

I always thought it was very elegant and simple, but powerful.

Schrodinger's Equation. Because no one understands where it comes from, and it tells us so damn much.

The golden mean is my fav of all time

http://www.vashti.net/mceinc/golden.htm

PV = nRT

Merely for the reason that I read it as "pervert".

x^n + y^n = z^n where n is all integers > 1.

Pythagorean Theorem.

a^2 + b^2 = c^2

Because I just love triangles. And it's the most used formula in my math classes.

I don't know about my favorite, but I've found that F=ma and e=mc² have always been pretty helpful in school.

The sine and cosine laws.

Those are very helpful for alot of engineering problems. :thumbsup:

(theta) = tan^(-1) ((v^2)/(rg)) is a good one too for Centrifugal acc.

There are so many neat theorems, but I'd have to say Noether's is my favorite. It essentially states that any continuous symmetry has a conserved quantity associated to it. In newtonian mechanics, this shows that the conservation of energy is equivalent to saying that our label for time=0 is arbitrary. Similarly, momentum conservation comes from invariance under translations and angular momentum conservation is equivalent to rotational symmetry.

Well, I've always loved this one:

http://members.optusnet.com.au/peterlmolloy/cossin.gif

And this is just wonderfull, just for the fact that it actually works.

http://members.optusnet.com.au/peterlmolloy/eipi.gif

Schrodinger's Equation equation is great too. We do know where it comes from though, it is essentially a conservation of energy relationship. We're just not sure why it works.

http://members.optusnet.com.au/peterlmolloy/schrod.gif

Are you just using this to find a good answer to the Google Labs Aptitude Test (GLAT)?

namnori, just in case that wasn't a joke: No!

To be totally childish for a second, I'd have to say

6922251 x 8

would have to be one of my favorites.

Seriously though, I love the projectile motion equations. It's fun trying to convince students that X and Y are independent of each other.

(sigma)F=0

Few are as simple and as useful.

I'd have to say Newton's Law of Gravitation and the oh so similar Coulomb' Law. They're both so useful and lead to so many different things.

1+1=2

You can't beat the classics.

Quadratic equation, cause it's the only formula that I can say off the top of my head without thinking for a second, I even have to think to remember the formula for the area of a rectangle.

-b(plus/minus) (the square root of(b^2 -4ac))/2a

Used to find the roots of a formula in the form of:

ax^2 + bx + c

My favorite is the slope of a line y=mx+b. Or how about perimeter of a square 2(l+w)

The special case of the Euler equation has been my favorite since third year of college:

<i>e</i>^<i>i</i>&pi;=-1

If it's a square wouldn't the perimeter just be 4*a, where "a" is the length of a side?

Yea, woops! Of course, if its a sqare all the sides would be even. I meant rectangle.

the Maxwell equations. The look good and considering they're like 160 yeas old make's it an impressive discovery.

Integration of e^x = e^x .

It strike me because the integral of e^x gave you back the same e^x. I thought it was special.

And it reminded me of a joke in Tilted Humor, I think it's the geek joke thread.

e^x is also its own derivative. It boggles the mind.

Wait... some number raised to all integers greater than one, plus another number raised to the same, equals a third number raised to same. What would you use that for? And does that mean that x can be raised to any integer n, or is raised to all simultaneously?

Baby, the limit as you and i approach the future is infinity.

6 x 7 = 42

Douglas Adams rules.

no!

6 x 9 = 42

x^n + y^n != z^n for all integers n > 2, for any integers x,y,z.

EDIT: I have a truly marvelous proof of this, but it won't fit into this text box.

I think the fundamental theorem of calculus is quite amazing actually:

The integral of a function is the anti-derivative of that function. It is absolutely amazing that that works.

It's fermats formula. There's no xyz integer solution for n>2. Get it right, or else you lose the hole point.

Buahahahh...awesome. :lol:

Yes, it is 6x9 = 42. And yes, as Douglas Adams himself said: "No one makes jokes in Base 13." :)

Personally, I like Gauss's Formula. Makes my summations easier.

mine's pretty obvious

The Euclidean Algorithm and the properties of e !

The shortest distance between two points is a straight line in the opposite direction. Don't know the formula yet.

<table bgcolor=white><tr><td>http://mathworld.wolfram.com/eimg3071.gif</td></tr></table>

FOIL - first one i remember learning. for those that may have forgotten, although nobody probably has:

F - first
O - outer
I - inner
L - last

i'm definitely an algebra person, geometry sucked!

OK, what does this formula do? I can't for the life of me remember this formula? Algebra manipulation?

When you are multiplying two binomials:

(a + b)(c + d)

do First terms (ac); Outer terms (ad); Inner terms (bc); Last terms (bd). Gives

ac+ad+bc+bd.

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Its so elegant, what with its partial derivatives...