- #71

#### strangerep

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You're too late. @Samy_A already entered that one. (You've got to check the whole thread before posting an entry... )Cauchy's Integral Formula:

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- #71

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You're too late. @Samy_A already entered that one. (You've got to check the whole thread before posting an entry... )Cauchy's Integral Formula:

- #72

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I don't know what this means but here it is:

- #73

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Since no one specified that the equation had to be a math equation, have a chemical equation:

- #74

that no three positive integers a, b, and c can satisfy the equation a^n + b^n = c^n for any integer value of n greater than two.

It is extremely simple to understand,

But urges anyone who reads it to prove it!

Beware, it is not as easy as it looks

Also, it holds the world record of being the longest standing problem(365 years) and being proved incorrectly for most number of times!

- #75

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Simple equation or oxygen molecule? You decide:

O=O

O=O

- #76

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"S" stands by action( S=∫dtL) ,this is the Least Action Principle.

All the physics lies in this equation. Equations of motion,symmetries and conservations can be extracted from that.

Ps: This quote is a free translation, i read it in a brazillian book.

- #77

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If there's any Bieber and Miley fans out there in physics land... I reckon I'm onto a winner

- #78

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[tex]e=\lim _{n\rightarrow \infty }\left(1+\frac{1}{n}\right)^n[/tex]

- #79

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Equation of a circle, written as circle.

- #80

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The only thing prettier than this is the proof of this equality.

Can you prove it without going to 2 dimensions?

- #81

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Can you prove it without going to 2 dimensions?

Yes, that's definitely possible.

- #82

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Yes, that's definitely possible.

Give me a clue?

- #83

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Give me a clue?

Differentiation under the integral sign and limit-integral theorems.

- #84

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I love this because it neatly summarizes things you learn in introductory calculus such as FTC, classical Stokes theorem, divergence theorem.

It's also really aesthetically beautiful- the latin d signifying the exterior derivative turns into the greek ∂ signifying the boundary of the manifold

- #85

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These may be of interest here, too,Regarding aesthetics in quantum mechanical expressions, we had a thread from a tattoo artist in the Quantum Physics forum not too long ago which may be of interest to the readers here.

http://www.concinnitasproject.org/portfolio/

- #86

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Love=You+I :v

- #87

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got it all jumbled up...

- #88

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[itex]H_2O[/itex]

If you don't appreciate it, then you don't appreciate**life**...

If you don't appreciate it, then you don't appreciate

- #89

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I appreciate having more than one molecule of it.

- #90

- #91

Minimalistic but very pleasing

[tex] \nabla^2 = \Delta [/tex]

[tex] \nabla^2 = \Delta [/tex]

- #92

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[itex]H_2O[/itex]

If you don't appreciate it, then you don't appreciatelife...

Not really an equation...

- #93

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No Gauss-Bonnet yet??

- #94

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You still seem to be thinking in terms of beauty-in-meaning, rather than visual beauty.No Gauss-Bonnet yet??

Actually, it's fascinating how high powered mathematicians like yourself and A. Neumaier (to name just 2 among others in this thread) perceive beauty-in-meaning where others do not, yet have trouble perceiving the visual beauty that others can. Other types of people (e.g., conventional artists) suffer the reverse -- they create beautiful pictures yet cannot even understand how basic percentages work.

- #95

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You still seem to be thinking in terms of beauty-in-meaning, rather than visual beauty.

Actually, it's fascinating how high powered mathematicians like yourself and A. Neumaier (to name just 2 among others in this thread) perceive beauty-in-meaning where others do not, yet have trouble perceiving the visual beauty that others can. Other types of people (e.g., conventional artists) suffer the reverse -- they create beautiful pictures yet cannot even understand how basic percentages work.

I'm not a mathematician nor a physicist, only a physics student, but I still feel like micromass.

Also, let's take a look at others. A good percentage of people posted some explanation along with their equations, which means they had some meaning in mind when they posted it.

The most voted equations are the ones by Samy_A and micromass himself, which are both more about the meaning than the looks.

It seems most of the people actually feel the same as micromass about the equations but they either don't know it or don't want to admit it!

Actually this is reasonable. How people feel about an equation gets stronger and stronger as they work with it and learn more about it and its relation with other equations, to the point that this meaning-induced feeling will over-shadow any feeling related to only the looks of an equation. Even about people who don't know the meaning and are just learning it from the explanations given, the meaning is more exciting than the looks!

- #96

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Don't forget the "all 1" formula from @TeethWhitener. It has the most votes currently.The most voted equations are the ones by Samy_A and micromass himself, which are both more about the meaning than the looks.

micromass' formula has small and capital pi in it.

- #97

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Oh...missed that one!Don't forget the "all 1" formula from @TeethWhitener. It has the most votes currently.

micromass' formula has small and capital pi in it.

Anyway, I think even that equation actually seems more interesting to people than beautiful!

P.S.

Aren't they asymptotic to each other rather than equal?

- #98

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Both values are the limit of the shown procedure. Those limits are equal.

- #99

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Don't forget the "all 1" formula from @TeethWhitener.

That one should definitely deserve to be the winner. But let's but honest, would it be as beautiful to somebody who didn't know what division and square roots are? Or to somebody who doesn't realize those are limiting processes? Because it's very hard to suppress this knowledge when judging the formula...

- #100

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Not really an equation...

well before me someone had posted some chemical bonds and the process of electrolysis was shown in the

Common, the most beautiful formula is this one:

[itex]L = i \bar{\psi}_i \gamma^\mu D_\mu \psi_i -\frac{1}{4} \sum_{b \in \text{adjoint}} \sum_{a\in U(1),SU(2),SU(3)}F^{ab}_{\mu \nu}F^{ab~\mu \nu} + Y^{ij} \bar{\psi}_i H \psi_{j} + + | D_\mu H |^2 + \mu^2 H^\dagger H - \lambda ( H^\dagger H)^2 [/itex]

- #101

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∫e^{x} = f(μ)^{n}

Here is one I think is beautiful!

Here is one I think is beautiful!

- #102

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Now you have to show that it is either generally true in some way or defines something meaningful.

- #103

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Now you have to show that it is either generally true in some way or defines something meaningful.

I think most people would consider it true. I just don't get why this forum allows it...

- #104

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Whereas a lot of these equations require an advanced degree to appreciate, this one is one that middle schoolers might appreciate more∫e^{x}= f(μ)^{n}

Here is one I think is beautiful!

- #105

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