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Favorite Equation Of All Time?

  1. Feb 12, 2010 #1
    What is your favorite mathematical equation/value of all time? Mine is e[tex]^{i\pi}[/tex], which equals -1.
     
  2. jcsd
  3. Feb 12, 2010 #2
    I second that.
     
  4. Feb 12, 2010 #3
    I've always had a soft spot for Stokes' Theorem; differential forms version:
    \int_{\partial \cal C} \omega = \int_{cal C} d\omega
     
  5. Feb 12, 2010 #4
    j = gmpy.divm(xyz[1]**(gen)-dp,yx,xyz[1]**(gen))//xyz[1]**(gen-ONE)
     
  6. Feb 12, 2010 #5
    x2-2x+3
     
  7. Feb 13, 2010 #6

    Mentallic

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    [tex]d=\left|\frac{ax_1+by_1+c}{\sqrt{a^2+b^2}}\right|[/tex]

    - 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...
     
  8. Feb 13, 2010 #7
    I would like to change my original thought.

    May favourite is by far this:

    [tex]\int_{all time}dt[/tex]
     
  9. Feb 13, 2010 #8

    uart

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


    [tex] 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 [/tex]
     
  10. Feb 13, 2010 #9
    call me a traditionalist, but its got to be E=mc^2
    its engraved on my ipod :)
     
  11. Feb 13, 2010 #10
    how about functions expressed using Hankel's wacky contour:

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

    [tex]\zeta(s) = \frac{\Gamma(1-s)}{2\pi i}\int^{+\infty}_{+\infty}\frac{(-x)^s}{e^{x}-1}\frac{dx}{x}[/tex]
     
    Last edited: Feb 13, 2010
  12. Feb 13, 2010 #11
    1=2.
     
  13. Feb 13, 2010 #12
    Mine is

    All Time = 3pi/2 + 5
     
  14. Feb 13, 2010 #13

    hotvette

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    y = xx. It has a minimimum at x = 1/e.
     
  15. Feb 15, 2010 #14
    Why does everyone love e^i*pi = -1 so much? Because Feynman liked it? Have some originality, people :)
     
  16. Feb 15, 2010 #15
    ^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!
     
  17. Feb 15, 2010 #16
    How about

    [tex]
    0 \neq 1
    [/tex]

    Without this, maybe mathematics would not exist? :smile:

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

    [tex]
    \log(\det(A)) =\mathrm{tr}\log(A)
    [/tex]

    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
  18. Feb 15, 2010 #17
    e[tex]^{i\pi}+1=0[/tex]

    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
  19. Feb 15, 2010 #18

    I'll second this one.
     
  20. Feb 15, 2010 #19
    My favourite would be the time-independent Schrödinger equation

    [tex]\hat{H} \psi = E\psi[/tex]​

    in this deceptively simple form :p
     
  21. Feb 15, 2010 #20
    Uhm i think you got that one wrong. e^(i*pi) = -1 , not +1
     
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