Favorite Equation

Do you guys have a favorite equation?

Mine is e^(i*pi)+1=0.

At the moment, the Gross-Pitaevskii-equation.

Originally posted by amolv06
Mine is e^(i*pi)+1=0.

That is a nice one, though you could argue it's an identity rather than an equation. If you wanted to be picky. 🙂

F = M/2 +7

A formula for determining how young you should date. If you're 30, then 1/2 of that is 15, +7 is 22. Avoid the 21 and under crowd.

Originally posted by AThousandYoung
F = M/2 +7

A formula for determining how young you should date. If you're 30, then 1/2 of that is 15, +7 is 22. Avoid the 21 and under crowd.

Neither my father nor sister followed that equation, and so far have had quite successful marriages.

Originally posted by twhitehead
Neither my father nor sister followed that equation, and so far have had quite successful marriages.

What were your parents' ages when they started dating?

One of the most interesting equations, and one of the most famous ones too, I believe, is this:
a^n + b^n = c^n, where a,b,c is an integer >0 and n is an integer >2.
Fermat got interested in it, and myriads of mathematicians thereafter.

One of the matematicians working with this equation is Sophie Germain (1776 - 1831) who has one of the most interesting life stories. She was a lady matematician in the area no women worked before. There is even a set of integers that is named after her.

The problem is now solved: There are no a,b,c, and n that can solve the equation. This is not interesting. What's interesting IMHO is that a seemingly simple equation is so difficult to deal with. Not many mathematicians can understand the proof. But in its simpler form it is understandable for amateur mathematicians. Like the case n=4 and some more.

Simon Sing brought the attention to this equation in his book "Femat's Last Theroem".

Originally posted by AThousandYoung
What were your parents' ages when they started dating?

I don't know exactly but about 41 and 21.

One of my favorites: B4IFQ(RU/18)

http://en.wikipedia.org/wiki/Maxwell%27s_equations#General_formulation

Originally posted by mtthw
That is a nice one, though you could argue it's an identity rather than an equation. If you wanted to be picky. 🙂

An identity of what?

Originally posted by talvtal
An identity of what?

A mathematical identity is one that remains constant regardless of the values of the variables in it.

ex.

(sin(A))^2 + (cos(A))^2 = 1

no matter what value you substitue for "A" the equation is true.

although now I'm slightly confused because there are no variables in e^(pi*i) = -1

?

Edit: ok actually its just a special case (x=pi) of

e^(ix) = cos(x) + i*sin(x)

Originally posted by joe shmo
A mathematical identity is one that remains constant regardless of the values of the variables in it.

ex.

(sin(A))^2 + (cos(A))^2 = 1

no matter what value you substitue for "A" the equation is true.

although now I'm slightly confused because there are no variables in e^(pi*i) = -1

?

Edit: ok actually its just a special case (x=pi) of

e^(ix) = cos(x) + i*sin(x)

And while im at it

I don't have a favorite yet, but one i'm currently looking at

y" + (k^2)y = 0

its soluion relates to Eulers identity.

Originally posted by joe shmo
A mathematical identity is one that remains constant regardless of the values of the variables in it.

Don't all equations have that property?

Originally posted by twhitehead
Don't all equations have that property?

Contrasting with an equation, which is true for particular values. A simple example:

2x = x + x, is an identity
2x = x + 1, is an equation with the solution x = 1.