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Featured Contest: Equations as Art 2017

  1. Sep 20, 2017 #1
    The goal is to create the most beautiful or interesting equation aesthetically (pleasing to the eye).
    This is not about it's mathematical significance. Get your inner designer on!

    • Each member is allowed to post one equation
    • The equation can be completely made up
    • Must use LaTeX
    • Be creative!

    To vote for an equation simply click the "like" button. You can vote more than once. The contest will close next Wed Sep 27th.

    The winner will receive a PF T-Shirt!

    ps. do not try to register new usernames for more entries or for likes. It's painfully easy to figure these out.

    Have fun! Go!
     
  2. jcsd
  3. Sep 20, 2017 #2

    Orodruin

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    I find it difficult to disregard meaning when it comes to aesthetically judge an equation so I will go with Stokes’ theorem for integration of differential forms. Both for its aesthetics in terms of its integral signs, simplicity in the form of the ##\omega##s appearing on both sides, and meaning:
    $$
    \int_{M} d\omega = \oint_{\partial M} \omega
    $$
     
  4. Sep 20, 2017 #3

    fresh_42

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    With the Fibonacci sequence ##F_n##, the Lucas sequence ##L_n## and the Catalan sequence ##C_n##
    $$
    \sum_{n\in\mathbb{N}}\frac{1}{n}\cdot\frac{1}{n}\cdot \frac{1}{n+1} \cdot \frac{F_n \cdot L_n}{C_n} = \frac{(2\pi)^2}{\sqrt{5}^5}
    $$
     
    Last edited: Sep 24, 2017
  5. Sep 20, 2017 #4
    This is a fun thread! I agree with @Orodruin that much of the beauty comes from the meaning; so I will go with an extension of the Cauchy integral formula.
    $$\oint\frac{f(z)\;dz}{\left(z-z_{0}\right)^{n+1}}=\frac{2\pi i}{n!}f^{(n)}(z_{0})$$
     
  6. Sep 20, 2017 #5

    Mark44

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    Here's one I like:

    $$\int~e^x = f(u^n)$$

    You might need to think about this one a bit ...
     
  7. Sep 20, 2017 #6
    I think I saw this on a T-shirt once. :biggrin:
     
  8. Sep 20, 2017 #7

    Orodruin

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    This is one of the few cases where the equality no longer holds if you actually perform the integral ...
     
  9. Sep 20, 2017 #8
    Finally an equation that makes sense. Looks like I have a future in mathematics after all.
     
  10. Sep 20, 2017 #9

    OCR

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    It looks difficult and unpleasant to me... :oldtongue:
     
  11. Sep 21, 2017 #10

    martinbn

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    Only if you are very young and think that girls have cooties, or very old and can remember the how but not the why.
     
  12. Sep 21, 2017 #11

    Ygggdrasil

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    ##3987^{12} + 4365^{12} = 4472^{12}##
     
  13. Sep 21, 2017 #12

    Orodruin

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    For some strange reason I don't buy it ...
     
  14. Sep 21, 2017 #13

    Ygggdrasil

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  15. Sep 21, 2017 #14

    Orodruin

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    Which you are of course in your full right to do. Just saying I agree it is a valid contest entry, but not a valid actual equation. :smile:
     
  16. Sep 21, 2017 #15
    thanks Yggg, that is a great story
     
  17. Sep 21, 2017 #16

    ohwilleke

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    Ha! Ha! Ha! (already familiar with the backstory).
     
  18. Sep 21, 2017 #17

    ohwilleke

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    e + 1 = 0
     
  19. Sep 21, 2017 #18

    fresh_42

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    This one is the beauty in the contest and will always win, if mathematicians are honest with their votes, I think. I like the positive form ##e^{i\pi}+1=0## a little more, as there is also the ##0## involved: top of the pop, so to say. And I really have to fight myself, because I still have two other beauties in mind ... d... rule ##1## ...
     
  20. Sep 21, 2017 #19

    Buzz Bloom

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    This was my mantra for a while.

    e + 1 = 0
     
  21. Sep 21, 2017 #20

    PAllen

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    I'm willing to be the idiot and admit I don't get it.
     
  22. Sep 21, 2017 #21

    fresh_42

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    ##\int = S##
     
  23. Sep 21, 2017 #22

    OCR

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    You did see . :oldtongue: . right... ? .








    *Definition of arithmetic bugs:

    "They added to your troubles, subtracted from your pleasures, divided your attention, and multiplied like hell...!"

    Lol...
     
    Last edited: Sep 21, 2017
  24. Sep 21, 2017 #23
    This one's kinda purty:

    $$1+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{1+\ddots}}}}=\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\cdots}}}}$$
     
  25. Sep 22, 2017 #24

    Math_QED

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    You stole my profile picture :eek: (at least an equivalent form haha)
     
  26. Sep 22, 2017 #25
    $$(\Box+\mu^2)\psi = 0$$
     
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