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PF Contest: Equations as Art

  1. Mar 24, 2016 #1
    The goal is to create the most beautiful or interesting equation aesthetically (pleasing to the eye).
    This is not about it's significance.

    • Each member is allowed to post one equation.
    • The equation can be completely new and made up (doesn't have to be famous).
    • Be creative!
    • The equation must be valid and true.

    To vote for an equation simply click the "like" button. You can vote more than once. The contest will close next Thursday the 31st.

    The winner will receive a copy of Carlo Rovelli's new book "Seven Brief Lessons on Physics"

    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!
    Last edited by a moderator: Mar 27, 2016
  2. jcsd
  3. Mar 24, 2016 #2


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    This is a popular wavefunction describing pairs of entangled particles, called the Double Gaussian wavefunction. It has a lot of symmetry, is incredibly easy to work with, and to me, is easy on the eyes as far as joint wavefunctions go.
    Last edited: Mar 24, 2016
  4. Mar 24, 2016 #3
    ## a_n = \frac{(\frac{1 + \sqrt{5}}{2})^n - (\frac{1 - \sqrt{5}}{2})^n}{ \sqrt{5}} ##
    The Binet´s Fibonacci number formula, which produces de Fibonacci's sequence 0,1,1,2,3,5,... from powers of the golden ratio.
    Last edited: Mar 24, 2016
  5. Mar 24, 2016 #4


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    For all [itex]x \geq 0[/itex],
    [tex]\frac{x^{2} + 1}{x + 1} \geq 2 ( \sqrt{2} - 1 ) ,[/tex] and the equality holds for [itex]x = \sqrt{2} - 1[/itex].
    The problem is, I believe, the above algebraic inequality is more useful than Rovelli’s book. :wink:
  6. Mar 24, 2016 #5
  7. Mar 24, 2016 #6


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    I was going to go with De Moivre's Theorem, but simplicity beautiful and this is a classic. The Pythagorean Theorem is what first made me realize that math is so alluring.
    Last edited: Mar 25, 2016
  8. Mar 24, 2016 #7


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    $$\Delta\phi ~\propto\, \oint A \cdot dx$$Cf. The Aharonov-Bohm effect. I.e., the electron phase shift arising in a closed loop around a solenoid. This is also one of the most beautiful things in (theoretical and experimental) quantum mechanics, imho.
  9. Mar 25, 2016 #8
    t' = γt
  10. Mar 25, 2016 #9
    I am going to do something interesting.:smile:
    According the law of parallel universes,There can be different worlds with different laws.If in our world Einstein proved E=mc^2,then there's another world where Ainstein proved :

    That's beautiful,right ?

    P.S : You can't question it's validity.It's true about the parallel universes and hence questioning whether the equation has any existence has no basis:wink:
  11. Mar 25, 2016 #10
    e=mc2. The most brilliant equation I've ever seen and it kind of made me appreciate mathematics
  12. Mar 25, 2016 #11


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    Let's see who gets this first.. $$y=cos (x)+cos (2x) $$
  13. Mar 25, 2016 #12
    The continuity equation. An elegant, yet simple way to state one of physics most powerful laws, the conservation of mass.
    [tex]\frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \mathbf{v}) = 0[/tex]
  14. Mar 25, 2016 #13


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    ## \mathcal{R}_{\mu \nu}-\frac 1 2 \mathcal R g_{\mu \nu}=8 \pi \mathcal{T}_{\mu\nu}##
    "Matter tells spacetime how to curve...", ooops, only one equation, so only half the sentence!:wink:
  15. Mar 25, 2016 #14
    [tex] \frac {\lambda}{2 \pi} = \frac{\hbar}{m c}[/tex]
  16. Mar 25, 2016 #15
    The Schwarzschild solution can be considered as a global solution of the vacuum equations, Tμν = 0, i.e. Rμν = 0
    everywhere, even at r = 0. In this case, the Schwarzschild solution is called a black hole, since nothing can escape from the horizon at r = RS.

  17. Mar 25, 2016 #16
    Just a simple equation, F=ma, and so much physics and technology from it.
  18. Mar 25, 2016 #17
    ##d(x, y) = \sup \{\frac{\bar{d}_i(x_i, y_i)}{i}\}##

    This represents a metric on the topological product ##\prod_{i \in \mathbb{N}} X_i## of a countable family of metrizable topological spaces .
    Here ##x, y \in \prod_{i \in \mathbb{N}} X_i##, ##x_i, y_i \in X_i##, ##i \in \mathbb{N}## and ##\bar{d}_i## is the standard bounded metric on ##X_i##.
    This is a powerful metrization theorem in topology since it proves that the product of a countable family of metrizable spaces is itself metrizable, and can be used as the starting point for proving (one of my favorite theorems in mathematics) the Urysohn metrization theorem.
  19. Mar 25, 2016 #18
    an equation in physics giving the kinetic energy of a photoelectron emitted from a metal as a result of the absorption of a radiation quantum: Ek=hν−ω
  20. Mar 25, 2016 #19
    when studying the different areas in Physics, have you ever wondered why waves, cycles and oscillations appear to dominate our universe, from the distribution of matter in the CMB down to description of particles, and even further down for some (string theory).
    And it's not all, how come we, as conscious beings, find beauty when we combine them in symmetrical ways (music, combination of colors like in paintings, cyclic arrangements...)?
  21. Mar 25, 2016 #20
    [tex]\prod_{p~\text{prime}} \frac{1}{1 - p^{-2}} = \frac{\pi^2}{6}[/tex]

    Why is this beautiful? Well, on the left hand side, you have objects from arithmetic. Prime numbers, which are essentially determined by numbers divisible only through 1 and itself. On the right-hand side, we have an object from geometry. The number pi, which gives us the circumference and area of a circle. At first sight, these two are very elementary objects with no relation. But then we obtain this very strange, elusive and beautiful relation between such two objects.
    Contrary to ##e^{\pi i} +1 = 0## (which is essentially a definition and cannot be checked heuristically), this one can be checked heuristically. Just take as many primes as you want and calculate the product to see you get closer and closer to ##\pi##.
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