e^(i*pi)+1

No variables, though... :)

methinks not... i do believe they are ROUND.

(trollin for jesus)

-Tim

How could you leave out Euler's beautiful equation which relates 0, 1, e, i, and pi?

e^(i*pi) + 1 = 0

0.999999999999999... = 1

a^n + b^n != c^n
for non zero integers a,b,c and n > 2
known as Fermat's last theorem [mbay.net].

z0 = c, Zn+1 = Zn ^2 + c

I know, I know - don't complain about the options.

The formula for the derivative [utexas.edu]. Probably the basis for some of the most useful mathematics.

I just wish I could reproduce it here.

Girls requires time and money

GIRLS = TIME * MONEY

but if "time is money"

TIME = MONEY

we have that

GIRLS = MONEY^2

and if "money is the root of all evil"

MONEY = SQRT(EVIL)

this implies that

GIRLS = EVIL

Q.E.D
(quod erat demonstrandum)

this is my favorite: 0^0=1

I like Einstein's formula for success:

A = X + Y + Z

Where
A = Success
X = Work
Y = Play
Z = Keeping your mouth shut

Googled from here [asu.edu].

After applying some simple algebra to some trite phrases and cliches a new understanding can be reached of the secret to wealth and success.

Here goes.

Knowledge is Power
Time is Money and as every engineer knows,
Power is Work over Time.

So, substituting algebraic equations for these time worn bits of wisdom, we get:

K = P (1)
T = M (2)
P = W/T (3)

Now, do a few simple substitutions:

Put W/T in for P in equation (1), which yields:
K = W/T (4)

Put M in for T into equation (4), which yields:

K = W/M (5).

Now we've got something. Expanding back into English, we get:

Knowledge equals Work over Money.

What this MEANS is that:

1. The More You Know, the More Work You Do, and
2. The More You Know, the Less Money You Make.

Solving for Money, we get:

M = W/K (6)
Money equals Work Over Knowledge.

From equation (6) we see that Money approaches infinity as Knowledge approaches 0, regardless of the Work done.

What THIS MEANS is:

The More you Make, the Less you Know.

Solving for Work, we get

W = M x K (7)
Work equals Money times Knowledge

From equation (7) we see that Work approaches 0 as Knowledge approaches 0.

What THIS MEANS is:

The stupid rich do little or no work.

Working out the socioeconomic implications of this breakthrough is left as an exercise for the reader

For those that don't know where these come from/what they are:

F = ma : Newton's 2nd Law of motion, relating force (F) with mass (m) and acceleration (a).

Originally, written as: F = (d2)/(dt2)[ms] (2nd derivative of displacement with respect to time). Yes, m was left in the derivative, which jives today with relativistic motion (mass increases with velocity).

a^2 + b^2 = c^2 : Pythagoras' theorem, stating the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Actually, it is misnamed, since the relation was know to envery surveyor/engineer/builder worth his salt 1000 years before Pythagoras was born.

(pi)r^2 : Formula for the area of a circle

For those interested in the historical attempts to calculate pi, I might recommend A History of Pi [amazon.com] by Petr Beckmann. Be warned: the author makes no bones about his strong opinions on history, but it's an interesting read nonetheless.

e^x : exponential formula. Euler's number (2.7182...) raised to the x power.

Incidentally, how is e^(i*pi) + 1 = 0 not in the poll? It only related the 5 most important numbers in mathematics! You actually could have put e^(i*x) = cos(x) + i * sin(x), of which e^(i*pi) = -1 is a special case.

E = mc^2 : Energy (E) is equal to mass (m) multiplied by velocity of light (c) squared (yes, a very large constant).

Einstein's famous relation which follows from his work on special relativity. Most obvious demonstation is nuclear weapons, whereby a very small amount of mass is converted into a great deal of energy.

2^|S| > |S| : inequality (not an equation) which states that exponential functions are larger than linear for any non-negative number. |S| means abs(S) ie. abs(-5) = abs(5) = 5

T = $ : not sure what this is

CowboyNeal, Q.E.D. : ask Jon Katz

The reason I chose F=ma is because mechanical physics is one of the few equations out there that you can 'see' and think about; you are able to apply it in a useful manner to a variety of physical situations.

When I started college, I thought about double majoring in Computer Science and Physics (I loved both at the time, and was quite good at Physics in high school (5 on the AP)), but once the Physics moved out of the realm of mechanics (pretty much anything related to F=ma) into the area I term 'magic' (a.k.a. anything dealing with electromagnetic waves), I couldn't wrap my head around it anymore :( So Computer Science it was :)

K9P

Commonly found on fire hydrants

X = Y
X^2 = XY
X^2-Y^2 = XY-Y^2
(X+Y)(X-Y)= Y(X-Y)
X+Y = Y
2Y = Y
2 = 1

what happened?

F=ma : from physics. Some call it Newton's Second law (ymmv)

a^2=... : Elementary mathematics. Pythagoras's theorem. For high flighers you can say it is a special case of the triangle inequality for the usual metric in R^2.

pi r^2: area of circle embedded in R^2 using above metric.

e^x : exponential growth/ decay (depending on you level of paranoia)

E=mc^2 : Pakistan vi India (basically)

2^|S|>|S|: set theory. the cardinality of functions from a set S to the set {0,1} is `bigger' than the set S

T=$ : Finance, but more usual written as e^x or called `interest'.

CowboyNeal, QED : Not my area of expertise, but probably a major area of research.
---

The mathematically inclinded all know the famous equation:
e^(pi*i)=-1

Square both sides and you get:
e^(2*pi*i)=1

Take the natural log of both sides:
2*pi*i=0

Have fun killing your brain over that result :)

-

For almost all real numbers, a, consider the sequence of convergents of their continued fraction expansion, {P0/Q0, P1/Q1, ... Pn/Qn, ....}.

Lim {n->infinity} (Qn)^(1/n) = exp(pi^2/(12 Ln 2)).

That's my favorite equation.

P = IE

Electrical Power is equal to Voltage times the Amperage.

The integral of a differential k-form over the boundary of a manifold is equal to the integral of the exterior derivative of the k-form over the manifold itself.

This equation has everything you need to know about integral calculus. It's the fundamental theorem of calculus, Gauss' theorem, Green's theorem and every other integral related theorem you've ever seen in one equation.

mine is

M = (Q, sigma, delta, q0, F)

A deterministic finite state machine, made of Q (the finite set of valid state),
sigma (the set of valid tokens), delta (the partial mapping function), q0 (the initial
state, aka S) and F (the set of final states, a subset of Q)

Life = L(M); the proof is left as an excercise to the reader (Hint: you need to have debugging
scars on your forehead to appreciate this.)

The e^x equation reminded me of this old joke from college:

The constant "c" is wandering around town, very upset because he heard that the big, bad "d/dx" is also in town. The anxious "c" meets up with another character who's very relaxed.

"How can you be so relaxed? d/dx is going to come around and wipe us all out!" said c.

"Because I'm 'e^x'. Stick with me, c, and you'll be okay."

So c and e^x joined hands, and became c*e^x. Shortly after, a nasty derivative walks up to them. c*e^x stays very calm.

"Aren't you afraid of me?" the derivative asked.

c*e^x coolly replied, "We're c*e^x. You can't do anything to us, you derivative!"

"OH YEAH?" replied the derivative. " WELL, I'M d/dy!!!"

That reminds me of a cheer we used to chant at football games back at Georgia Tech:

E to the X dy dx,
E to the X dx,
Tangent Secant Cosine Sine,
3.14159,
Square roots, cube roots, Poisson brackets,
Dis-integrate 'em Yellow Jackets!

Read it and weap, guys:

[(pi)**(d/2) / (d/2)!] * R**d

Folks, you need to keep in mind first the following:

You all know that Factorial of n ("n!") is a product PI but since most of you are programmers I'll define it recursively:

n! = (n-1)! * n

Okay, that's simple enough.

Next, remember n! = Int(x**n / e**x dx, 0, [Inf]) which is a messed up way of expressing an integral, so let's just skip that step and cut to the chase:

Define the base case for your Recursive Function Factorial:

0! = 1

Now, since a line (d=1) or 3D space (d=3) are odd, you get for each:

[sqrt((pi)) / (1/2)!] * R

and

[pi * sqrt((pi)) / (3/2)!] * R**3

Yes, it's not 4/3 * (pi) * R**3 but be patient, we're almost there!!

Now let's write a special base case for half-factorial. We can evaluate the integral above at n=-1/2 and by rearranging to create a Gaussian curve, we find that:

(-1/2)! = sqrt((pi))

With our recursive definition, we see:

(1/2)! = (-1/2)! * 1/2 = sqrt((pi))/2
(3/2)! = (1/2)! * 3/2 = [3 / 4] * sqrt((pi))
...And So On

So, given that, we can solve d=1 and d=3 and any odd d, e.g.

d=1 => [sqrt(pi) * 2 / sqrt(pi)] * R = 2*R
d=3 => [(pi) * sqrt(pi) * 4 / (3 * sqrt(pi))] * R**3 = 4/3 * (pi) * R**3

Now for your slashdot option, you are SO 2-dimensional!!! Please consider:

[(pi)**(2/2) / (2/2)!] * R**2 = (pi) * R**2

And for you Four-Dimensional, Quaternian or simply Einstienian Space-Time Centrics, the Hyper-Volume of a HyperSphere in 4D is:

[(pi)**2 / 2] * R**4

And for Steven Hawkin and other String-Therory subscribers:

[(pi)**5 / 120] * R**10

Or if you like Membranes like me and are into M-Theory:

64/10395 * (pi)**5 * R**11

And it's all thanks to:

[(pi)**(d/2) / (d/2)!] * R**d!!

Devo Andare,

Jeffrey.

P.S. Because Slashdot.org does not recognize the need for mathematical formulae to be contained on separate lines and this serious post of bone-fide content is consider spammy because it originally got an 18.6 characters per line count, this disclaimer is included to let you, the reader enjoy this thoughtful commentary. That first sentence brought me up to 22.0 but I must continue with this rightly ignored gibberish in order to create something the Slashdot.org engine considers worth your time. I will continue writing until I reach the magic threshold. Sorry again for the added bandwidth of this silly post script, but after all, it would be VERY hard to read this if I didn't put all my mathematical formulae on separate lines, eh? Now, with 26.9 characters per line I still have a ways to go with my run-on sentences and endless paragraph, so shall I tell you a story? Would you like to know more about me? Like that my favourite television programme is Doctor Who, or that for some reason I perfer F=m*a over E=m*c**2 because the later is SO cliché and the former so cute because Einstein ended up proving in General Relativity that as you approach the speed of light, m goes to infinity really messing up the Newtonian calculation. And don't get me started on how you can't know the position and velocity at the same time to an order below Plank's Constant, but Heisenberg's Uncertainty Principal really doesn't enter into this, as I'll I'm interested in is expounding on the beauty of the universal HyperSphere formula for HyperVolume. Ta Da! Now it is long enough! Sorry you had to read this paragraph but I did warn you it was not worth it. :)

I always wrote F=m/a on the desks in Physics classrooms. Bump the less diligent students down the curve.

Newton really wrote (correctly):
F = dp/dt
where p is momentum = mv. This makes:
F = d(mv)/dt
and by the prodcut rule of differentiation:
F = m*dv/dt + v*dm/dt
and we all know that dv/dt = a, so we get:
F = ma + v*dm/dt
Now, the change of mass with respect to time of some object is usually zero, so the last term usually dissapears and the equation becomes F=ma, but in referential cases, when some object is moving closer and closer to the speed of light, the mass may grow as a function of velocity, so the last term might not be zero!