What Formula Would You Tattoo?

My_Skin_As_A_Cheatsheet asks this potentially painful question: "I have a friend/colleague who is planning on getting a tattoo in the next month or so. She has decided that this tattoo will be a mathematical or statistical formula, and has been scouring the web and books in recent weeks looking for a cool formula to put on her upper back/shoulder. If you could tattoo a single formula, axiom, etc. (from math, statistics, or any other similar field) on you, what would it be and why? Are there any you think are particularly profound or important? Cool symbols are a plus." Do you have a formula that means so much to you that you would get it tattoed onto your skin? If so, please share it with us. Please try to do you best in HTML (and I wish there was MathML support in something other than Mozilla...of course, Slashdot won't accept those tags anyways...yet!).

Comments

this one is nice...

[Jose]

e^(pi*i) + 1 = 0

that has always been one of my favourites. (mostly because it brings several important numbers into one small formula)

My personal favorite..

[cmowire]

I would tattoo the following:

Integral(E^x) = f(u^n)
Which becomes, when you look at it,
Sex = Fun

That would be my suggestion. ;)

Re:What you are looking for...

[grammar nazi]

Take your pick:

Algebraic fundamental formula: Although Euler's formula is very beautiful, I would opt for, the more algebraic, Lagrange's Theorem...

|G|=|H|[G:H]

Where H is a subgroup of a finite group G. Here is a theorem that is at the very basis of algebra and numbers.

Number thoery cool formula: Another equation that would be good for a tattoo is Hardy and Ramanujan's equation for the number of partitions of a number n, p(n). I will TeX the equation since I can't do it justice with HTML. If you don't use LaTeX, then refer to Number Theory, by George Andrews, p. 150 (it's a Dover book so it's $6.95 and excellent).

p(n)=\frac{1}{2\pi\sqrt{2}}\frac{d}{d n}\left{ \frac{\exp \left( \frac{2\pi}{\sqrt{6}} \sqrt{n-\frac{1}{24}} \right) }{\sqrt{n-\frac{1}{24}}}

An interesting thing about this equation is that it doesn't actually converge. You can make it converge to an answer by replacing the exp with a sinh and remove the 2 in the very first denominator, but Hardy and Ramanujan never figured that out.

Simple Chaotic Formula: One of the simplist equations to display a period 3 orbit, and hence chaotic behavior, is the logistic map:

f( x(n+1) )= 4 x(n) ( 1- x(n) )

I would recommend using subcripts in place of (n) and (n+1).

Fourier Series: Finally, nothing in mathematics is more beautiful and elegant than Fourier series. The following equation is at the heart of the MP3 piracy debate and it is responsible for most video and sound encoding. I don't know any equations for Fast Fourier Transforms, but here's one for the general Fourier series (in complex form, because that makes a better tattoo).

\Phi(x)=\sum^{\infty}_{n=-\infty} c_n e^{in\pi x/l}

For further reading in Fourier series (at an undergraduate level), I recommend Partial Differential Equations, an Introduction by Strauss

This slashdot story has inspired me to get a tattoo!

Re:Tattoo

[grammar nazi]

Ouch! Normally I'm the grammar nazi, but for this post I'm going to play stick-in-the-mud Nazi.

You're link is to an article that talks about hepititus. You can avoid this 100% by going to a reputable tattoo artist and not a hole in the wall place.

Finally I think that your comment about seeing a psychiatrist is a little overboard. I would hardly refer to a tattoo as currently cool and trendy.

Tattoos have been cool and trendy for hundreds of years now. They are here to stay. Hard mathematics has been accurate and around for hundreds of years. Thus, tattoos of hard mathematics are not a temporary fad.

Okay, my logic isn't 100% sound, but you get the point. Now shove off, pal!

And don't forget

[cperciva]

\int{\frac{1}{cabin} d(cabin)} = houseboat.

(For those who haven't seen this before, the left side evaluates to log cabin + C.)

Well....

[Fencepost]

I may come off sounding like a conservative old fart, but if this is her first tat and she doesn't already have something personally meaningful that she wants to use then perhaps she should reconsider getting (semi-)permanently inked.

Of course if she already has other tats and wants to add a formula as another but doesn't have anything particularly meaningful to her in mind, I think it'd be hard to beat Grey's suggestion or something patterned after it. Failing that, there are all sorts of interesting things to use from the simple, compact fundamentals to larger "unexpected" items. Ask one of the math faculty or a calculus student about curves where the area under the curve is infinite but the volume of the solid created by spinning it is finite.

If nothing else, she should keep in mind that she's likely to be asked semi-regularly what it means, and if she can't explain it she's going to end up feeling stupid. "Hey, what's the math tat mean?" "Um, I can't really explain it, I just thought it looked neat..."

-- fencepost

My vote

[AstroJetson]

Well, as others have pointed out, you can't beat the sheer elegance of Euler's Formula. But if her pain threshold is pretty high another worthy candidate would be...

In the beginning God said:

[insert Maxwell's equations]

...and there was light.