# Favorite Equation Of All Time?

1. Feb 12, 2010

### imagenius128

What is your favorite mathematical equation/value of all time? Mine is e$$^{i\pi}$$, which equals -1.

2. Feb 12, 2010

### Anti-Meson

I second that.

3. Feb 12, 2010

### linovari

I've always had a soft spot for Stokes' Theorem; differential forms version:
\int_{\partial \cal C} \omega = \int_{cal C} d\omega

4. Feb 12, 2010

### Mensanator

j = gmpy.divm(xyz[1]**(gen)-dp,yx,xyz[1]**(gen))//xyz[1]**(gen-ONE)

5. Feb 12, 2010

### MotoH

x2-2x+3

6. Feb 13, 2010

### Mentallic

$$d=\left|\frac{ax_1+by_1+c}{\sqrt{a^2+b^2}}\right|$$

- perpendicular distance between a point (x1,y1) and a line ax+by+c=0

I reckon the proof is so neat! Except no one else in my class appreciated it whatsoever when they learnt it...

7. Feb 13, 2010

### Anti-Meson

I would like to change my original thought.

May favourite is by far this:

$$\int_{all time}dt$$

8. Feb 13, 2010

### uart

Ok I'll post one just for fun. :)

$$f(x) = \frac{1}{2 \pi} \int_{-\infty}^{+\infty} \, \left\{ \int_{-\infty}^{+\infty} f(\lambda) \, e^{-i 2 \pi \omega \lambda} \, d\lambda \right\} \, e^{i 2 \pi \omega x} \, d\omega$$

9. Feb 13, 2010

### raymo39

call me a traditionalist, but its got to be E=mc^2
its engraved on my ipod :)

10. Feb 13, 2010

### fourier jr

how about functions expressed using Hankel's wacky contour:

$$\Gamma(z) = \frac{1}{e^{2\pi iz}-1}\int^{+\infty}_{+\infty}e^{-t}t^{z-1}dt$$

$$\zeta(s) = \frac{\Gamma(1-s)}{2\pi i}\int^{+\infty}_{+\infty}\frac{(-x)^s}{e^{x}-1}\frac{dx}{x}$$

Last edited: Feb 13, 2010
11. Feb 13, 2010

### Algr

1=2.

12. Feb 13, 2010

### Svalbard

Mine is

All Time = 3pi/2 + 5

13. Feb 13, 2010

### hotvette

y = xx. It has a minimimum at x = 1/e.

14. Feb 15, 2010

### IttyBittyBit

Why does everyone love e^i*pi = -1 so much? Because Feynman liked it? Have some originality, people :)

15. Feb 15, 2010

### ephedyn

^IttyBittyBit: I didn't know that Feynman liked it - where did you read that from? Now I've more reason to like it. Coincidentally, it's the 15th of February today. He passed away exactly 22 years ago. :(

I like it for the traditional reason though, that there's e, i, pi, 0 and 1, ^, *, +, = in a single equation!

16. Feb 15, 2010

### torquil

$$0 \neq 1$$

Without this, maybe mathematics would not exist?

One of my lecturers in quantum field theory said that the most important (consider path integrals) equation in physics is

$$\log(\det(A)) =\mathrm{tr}\log(A)$$

One of my personal favourites are

EDIT: A picture was supposed to appear here... Anyway, it was the formula that expresses e as a continued fraction. I won't bother to write it myself.

Torquil

Last edited: Feb 15, 2010
17. Feb 15, 2010

### matheinste

e$$^{i\pi}+1=0$$

This has been described as the mathematical poem, linking the sometime called big five of mathematics, e, pi, i, 0 and 1. When you consider that it involves an irrational number raised to an imaginary irrational power being equal to unity, it is, at first sight, to a non mathematician like myself, truly magical. Of course when you know a little more mathematics it is quite simple, no magic involved.

Matheinste.

Last edited: Feb 15, 2010
18. Feb 15, 2010

### Phyisab****

I'll second this one.

19. Feb 15, 2010

### Fightfish

My favourite would be the time-independent Schrödinger equation

$$\hat{H} \psi = E\psi$$​

in this deceptively simple form :p

20. Feb 15, 2010

### Svalbard

Uhm i think you got that one wrong. e^(i*pi) = -1 , not +1