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Thank you for your suggestions on the swag ideas. For our math community, we'll be sending top users (first 2 pages of all time, sorted by rep) coffee mugs and a writing pad.

Below is a mockup up of the design.

Math SE swag design

For the design, I think it's more appropriate to emphasize the math aspect; so I'm using Euler's Identity as the main focus.

Of course, I'm not a mathematician, if you have a suggestion for another equation/theorem, please let me know. Please do keep in mind, the space is somewhat limited, so I prefer nothing too complex(from a design POV).

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    $\begingroup$ I really have no love for that identity... In any case, how did you typeset it? It looks very, very strange. TeX usually does a great job :) $\endgroup$ Commented Jul 1, 2011 at 20:00
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    $\begingroup$ @mariano can you perhaps suggest another equation that you could perhaps love, in some alternate reality where such things are possible? $\endgroup$ Commented Jul 1, 2011 at 20:10
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    $\begingroup$ @Jin: What font is $e^{i\pi}+1=0$ rendered in, in that image? $\endgroup$
    – Isaac
    Commented Jul 2, 2011 at 21:26
  • $\begingroup$ I am curious to know: Is there anyone who has not spent some quality math time in the US who appreciates this way of writing Euler's equation? $\endgroup$
    – Phira
    Commented Jul 3, 2011 at 9:40
  • $\begingroup$ @thei I found this form in a youtube video. As I said, I'm not a mathematician. This is just for to get the conversation started. @Isaac for the final design I'll be using STIX font. The one in the mockup isn't accurate. $\endgroup$
    – Jin
    Commented Jul 3, 2011 at 17:51
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    $\begingroup$ @Jin: Here is a PDF (STIX font, editable) of the formula rendered with commercial math typesetting software and here is a PNG of that PDF. Rendering the same equation using Minion Pro instead of the STIX font yields this PDF or this PNG. $\endgroup$
    – Isaac
    Commented Jul 3, 2011 at 18:41
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    $\begingroup$ @Isaac: ($e$ and $i$ and should really be set in an upright font, as all constants... $\pi$ too, but that is less significant as most upright greek fonts are pretty italic) $\endgroup$ Commented Jul 3, 2011 at 19:36
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    $\begingroup$ @Mariano: Whether constants are set in roman or italics is a style convention—I am inclined to set any alphabetic letters used singly in a mathematical expression in italics to distinguish them from surrounding roman text. The $\pi$ is set in roman type. $\endgroup$
    – Isaac
    Commented Jul 3, 2011 at 20:27
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    $\begingroup$ We also need a much better logo. $\endgroup$ Commented Jul 3, 2011 at 22:58
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    $\begingroup$ Some of those who added answers to this question, with proposals, are deleting them. Please note that the negative votes only indicate (or are supposed to only indicate) disaggreement with the proposal! $\endgroup$ Commented Jul 4, 2011 at 0:07
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    $\begingroup$ @Jin: What is the current swag status? $\endgroup$ Commented Oct 31, 2011 at 16:49
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    $\begingroup$ @Jin: I'd also like to know the current swag status. Do we need to make a final determination on the design? Are t-shirts still going to be offered? $\endgroup$ Commented Dec 29, 2011 at 13:12
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    $\begingroup$ @Jin: People have asked questions regarding the "Swag" and even I would like to know the status. Why have haven't you replied for the above comments. $\endgroup$
    – user9413
    Commented Feb 25, 2012 at 19:54
  • $\begingroup$ If possible I would like to know if this topic was forgotten. $\endgroup$ Commented Mar 22, 2012 at 19:37
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    $\begingroup$ We haven't forgotten about this, but the designs proposed here are... Not good for putting on physical items. We're going to go with the usual logo + url, and the standard package of top user items + one additional item to make up for the long wait - stay tuned for details and pics in the next few days. $\endgroup$
    – Shog9
    Commented Mar 23, 2012 at 18:11

10 Answers 10

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The picture at https://mathoverflow.net/questions/8846/proofs-without-words/8847#8847 seems to have many adepts. (I would redraw it without the arrows if I had to do it again...)

The image can be regenerated in, say, SVG form with the following Mathematica code

picture[n_, {i0_, j0_}, cs_] := 
  Graphics[{
    EdgeForm[{Thickness[0.0015], Black}],
    Table[{
      FaceForm[{
      Which[
        {i, j} == {i0, j0}, cs[[4]],
        {i, j} == {i0, 0} || {i, j} == {i0 + j0, 0}, cs[[3]],
        j == 0, cs[[2]], 
        True, cs[[1]]]
        }],
      Disk[
        i/n {1, 0} + j/n {Cos[\[Pi]/3], Sin[\[Pi]/3]},
        1/(2 n + 2)
        ]
      },
      {i, 0, n}, 
      {j, 0, n - i}
      ]
    }
  ];
g = With[{colors = colors = ColorData[14]},
  picture[6, {2, 3}, {colors[4], colors[8], colors[7], colors[3]}]
  ];
Export["picture.svg", g, ImageSize ]

which produces (after converting to PNG: I don't seem to be able to upload an SVG image here...) this:

enter image description here

This is the one I would choose (I cannot vote on it though!)

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    $\begingroup$ Yes, as I said in a previous comment, this picture would look really nice on a coffee mug. Having equations is fine, but coffee mugs are all about the pictures they have. At least I would certainly be willing to buy a coffee mug with this picture on it, but probably wouldn't buy one with Euler's identity on it =P $\endgroup$ Commented Jul 3, 2011 at 20:07
  • $\begingroup$ A writing pad with Euler's identity looks fine to me. But I do like this picture. $\endgroup$ Commented Jul 17, 2011 at 16:27
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My preference tends towards the geometric and visual rather than text. So I voted up Mariano's binomial-counting-formula. But I'd also be keen to take something from an actual MSE thread. Perhaps the tessellation thread:

https://math.stackexchange.com/questions/36834/can-someone-explain-the-math-behind-tessellation

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This would be nice:

$1+2+3+\cdots = -\frac 1 {12}$

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    $\begingroup$ I like this one because the notation is easy enough for people less experienced with math to go, "That's clearly not true, what's going on here?" and then gives one the opportunity to explain what it really means. $\endgroup$
    – yunone
    Commented Jul 2, 2011 at 20:10
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    $\begingroup$ I would actually prefer an equation that makes mathematical sense and is not just a game with symbols. I never understood people's obsession with that silly "identity". And by the way, how is that better than $1+2+ 4+ 8 + \cdots = -1$ which is much easier to explain and just as silly? $\endgroup$
    – t.b.
    Commented Jul 3, 2011 at 9:02
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    $\begingroup$ @Theo: I find values of the analytic continuation of the zeta function more interesting than the identity "1/(1-2)=-1". $\endgroup$
    – Phira
    Commented Jul 3, 2011 at 9:36
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    $\begingroup$ Me too, but then $\zeta(-1) = - \frac{1}{12}$ would be the right thing to write and not the infinite sum. Otherwise I really don't see a difference. $\endgroup$
    – t.b.
    Commented Jul 3, 2011 at 15:45
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    $\begingroup$ "$1+2+3+\cdots = -\frac 1 {12}$ under my theory. If I tell you this you will at once point out to me the lunatic asylum as my goal." -S. Ramanujan's second letter to G.H. Hardy, 27 February 1913. $\endgroup$ Commented Jul 18, 2011 at 4:29
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Despite being beaten, my favorite math picture are complex dynamics fractals, especially the Newton fractal. A nice rendering is the one in http://cosec.bit.uni-bonn.de/?id=642. enter image description here

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This one: $$ \int_{-\infty}^\infty e^{-x^2}\,dx = \sqrt{\pi} $$

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    $\begingroup$ Or perhaps the form I have found very useful $$\large\int_{-\infty}^\infty e^{-\pi x^2}\;\mathrm{d}x=1$$ $\endgroup$
    – robjohn Mod
    Commented Nov 17, 2011 at 2:48
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The equality $$196884=196883+1$$ is a pretty amazing one , although somewhat cryptic :)

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Two examples of lovable, space ocupying equations:

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    $\begingroup$ @Theo: There is a mathematical field called "Moonshine theory" and no one told me about it?? Any other alcoholic notions that I am unaware of? ;-) $\endgroup$
    – Asaf Karagila Mod
    Commented Jul 2, 2011 at 21:05
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    $\begingroup$ I'm in favor of the picture in Mariano's link instead of having Euler's identity. A coffee mug without a nice colorful picture is not very attractive to eye. By the way, this one is really funny =P $\endgroup$ Commented Jul 3, 2011 at 5:31
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    $\begingroup$ @Mariano You should have separated the equations for voting purposes. It would be interesting to know which equation people actually would like on their mugs. I would totally want the moonshine one while the Jacobi triple product has the same problem as the proposed Euler's equation: It has very different presentations and it really rubs you the wrong way if the presentation is counter to your preferred point of view. $\endgroup$
    – Phira
    Commented Jul 3, 2011 at 9:39
  • $\begingroup$ I exploded this into several answers (and now the comments of course don't make much sense...) $\endgroup$ Commented Jul 3, 2011 at 19:14
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From Pappus’s theorem and elliptic curves by Terence Tao

enter image description here

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I am particular fond of https://mathoverflow.net/questions/3134/whats-your-favorite-equation-formula-identity-or-inequality/4680#4680

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I would go for:

  1. $\displaystyle ZFC+V=L\vdash 2^{\aleph_0}=\aleph_1$ (the continuum hypothesis is true in Godel's constructible universe)
  2. $\displaystyle \varnothing\Vdash \text{Math is fun!}$ (the empty condition forces that math is fun!)
  3. $\displaystyle 0\to\text{Coffee}\to\text{Mathematician}\to\text{Theorem}\to 0$ (a fatalistic and categorical description of Erdos' theorem about coffee as a short and exact sequence)
  4. $\displaystyle \mathbf{Math}\models\text{Fun!}$ (Mathematics is a model for fun!)

And so many others, and I would much rather any other the above over the Euler's formula (which I appreciate and respect, but to quote Sheldon Cooper "What is life without whimsy?")

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    $\begingroup$ Egads, I'd much prefer Euler's identity than any of that. With the possible exception (of a tie) with 3. $\endgroup$ Commented Jul 1, 2011 at 22:35
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    $\begingroup$ Though come to think of it, you shouldn't be using a short exact sequence. I'm okay with coffee being injective to Mathematicians, and Mathematicians being surjective onto Theorems is not quite okay, but acceptable. But the implication of "Theorem = Mathematician / Coffee" is, I think, the opposite of "Erdos' theorem"... $\endgroup$ Commented Jul 1, 2011 at 23:22
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    $\begingroup$ @Willie: What can I say... bunch of algebraists in this town. :-P $\endgroup$
    – Asaf Karagila Mod
    Commented Jul 2, 2011 at 7:43
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    $\begingroup$ Agreed, a short exact sequence seems out of place. Shouldn't you just say something like $\text{Mathematicians} \cong \text{Hom}(\text{Coffee}, \text{Theorems})$? $\endgroup$ Commented Jul 3, 2011 at 22:12

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