LaTeX Spoken Here!

This is a test of LaTeX on the site*.

The first equation I shall try is the following (for more on unpacking this equation and its meaning, see this post and links therein):

[tex]u{\cal R}^2-\frac12 {\cal R}{\cal R}^{\prime\prime}+\frac14({\cal R}^\prime)^2=\Gamma^2\ .[/tex]

Yay! It works. I have implemented it in the comments too. So now we can have a new, sharper tool for our discussions and arguments.

Use: Type simple LaTeX commands enclosed between [ tex ] and [ / tex] (remove the spaces between the things in the square brackets) and it should work once you submit.

Enjoy.

-cvj

(*I got around the problems of not being able to have LaTeX running on my host. Hurrah! The compromise I used means that the LaTeX is not as nicely formed as it could be, but it’s good enough! Learn more about latexrender and mimetex here.)

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151 Responses to LaTeX Spoken Here!

  1. Clifford says:

    Test:

    [tex] \frac{1}{2}v^{\prime\prime}-v^3+zv+\frac12\pm\Gamma=0\ .[/tex]

    -cvj

  2. Melquiades says:

    Test:

    [tex] E = mc^2 [/tex]

    Hopefully it will work… This is great Clifford!

  3. Carl Brannen says:

    The preview doesn’t work, which means this is going to require some faith or care…

    [tex]\rho^2 = \rho[/tex] is the idempotency relation that defines particles in a density operator formalism. Example (chiral) solution:

    [tex]\rho = 0.25(1+\gamma_0\gamma_3)(1 – i\gamma_1\gamma_2)[/tex]

    Okay, apply prayer, and hit submit…

  4. Melquiades says:

    Awesome!

  5. Carl Brannen says:

    Wow, it’s even more of a trip when you can’t know with certainty that your tex is going to work in advance.

  6. Bee says:

    R_{\mu\nu} – \frac{1}{2} g_{\mu\nu} \mathcal{R} = 8 \pi G T_{\mu\nu}

  7. Bee says:

    [tex]R_{\mu\nu} – \frac{1}{2} g_{\mu\nu} \mathcal{R} = 8 \pi G T_{\mu\nu} [\tex]

  8. Clifford says:

    Bee…. put it between the things I mentioned in the post.

    -cvj

  9. Bee says:

    Okay. I can do it!

    [tex] R_{\mu\nu} – \frac{1}{2} g_{\mu\nu} \mathcal{R} = 8 \pi G T_{\mu\nu} [/tex]

  10. Bee says:

    πŸ™‚
    πŸ™‚
    πŸ™‚

  11. Clifford says:

    This is way more fun than it really should be, isn’t it? πŸ˜‰

    -cvj

  12. Bee says:

    This is indeed cool. Can it make integrals?

    [tex]S = \int d^4 x {\mathcal L}[/tex]

  13. Bee says:

    Wow! I’m impressed. I’ve regretted more than once that my blog is running on a public server. All that template stuff really sucks, it just never looks like I want it to. Btw, you probably know that your-css sheet is kind of messed up with MS internet explorer? It’s kind of a funny effect that I haven’t seen anywhere else. If the site gets too long, say more than 80 comments, the text keeps running out of the window, because it’s not totally horizontal.

    If I’d consider moving my blog elsewhere, what would you advise me to consider?

    B.

  14. Bee says:

    Gee! I meant to say: because it’s not totally vertical. Long day, I think I need to get some dinner. Have a nice evening. Best,

    B.

  15. Clifford says:

    Bee, I’ll email you about blogging options. For ease of use, you can use WordPress on any number of public hosting services, or on your own computer for full control of everything (I do that for my private reserch blog for example, where I’ve had latex prettily running for over a year now). Others will disagree. Jacques can quote you volume, chapter, and verse about why it would be better to use the sort of things he uses on golem…. for the best mathematics rendering. I’m happy with this less powerful solution….

    About IE. I don’t support it. I’ve heard that the most recent versions are better built and render the site more accurately.

    Best,

    -cvj

  16. Plato says:

    Bee,

    Cliffords site works okay with Firefox.

    Cosmic Variance is now encoutering some of the problems as well.

  17. Aaron F. says:

    Oooh, so much fun!

    [tex]\forall n \in \mathbb{Z}, n \geq 2, \exists F = \{ p \mid p \in \mathbb{P} \} \tex{s.t.} n = \prod_{p \in F} p[/tex]

    Fingers crossed…

  18. Aaron F. says:

    Wow… I can’t believe that worked the first time! A preview option is DEFINITELY a must, especially for schlemiels like me. πŸ™‚ The spacing is a bit wacky, but everything is legible, and I’m impressed with the handling of \mathbb{…} — I usually have to include \amsmath or something before it’ll work.

  19. [tex] \frac{\partial \phi}{\partial t} = \nabla M \nabla \mu [/tex]

    Keeping my fingers crossed!

  20. Lubos Motl says:

    [tex] P^{\alpha}(\sigma)=Z^{\alpha} = \sum_{k=-1}^{d-1} \beta^{\alpha}_{k+1} \sigma^k = \frac{\beta^\alpha_0}\sigma + \beta^\alpha_1 + \beta^{\alpha}_2 \sigma,\qquad f(x) = \int_0^\infty dt \frac{e^{-t}\sqrt{1+t^2}}{t+1} [/tex]

  21. Arun says:

    [tex]f_I(x_I)
    &=& \int_{-1}^\infty f_I(t) dE_I(t)
    =\int_{-1}^\infty [1+\sum_{n=1}^\infty
    \left( \begin{array}{c} q \\ n \end{array} \right) t^n]\;
    dE_I(t)
    \nonumber\\
    &=& [1+\sum_{n=1}^\infty
    \left( \begin{array}{c} q \\ n \end{array} \right) x_I^n]\;
    [/tex]

  22. Arun says:

    Hmm, the above was equation 2.6 of gr-qc/0607101 simply cut-and-paste here. Not sure what the & are doing in it πŸ™‚

    [tex]
    f_I(x_I) = \int_{-1}^\infty f_I(t) dE_I(t)
    =\int_{-1}^\infty [1+\sum_{n=1}^\infty
    \left( \begin{array}{c} q \\ n \end{array} \right) t^n]\;
    dE_I(t)
    \nonumber\\ = [1+\sum_{n=1}^\infty
    \left( \begin{array}{c} q \\ n \end{array} \right) x_I^n]\;
    [/tex]

  23. Arun says:

    [tex]\{\vec{C}(\vec{N}),\vec{C}(\vec{N}’)\}[/tex]

  24. Arun says:

    Please publish the recipe for how to do this.
    Thanks in advance!

  25. Clifford says:

    latexrender is a well known plugin. But if you don’t have latex on the server, you can sometimes get away by wrapping something similar to latexrender around mimetex.

    See this whole blog devoted to this. You have to tailor things a bit to get it to work, but it works.

    -cvj

  26. Clifford says:

    Ok Lubos, just this once a comment of yours can stay. Just finished assigning grades for my course and so I am oozing with good will. πŸ™‚

    -cvj

  27. Clifford says:

    [tex]\Large\overbrace{a,\ldots,a}^{\text{k a^,s}}, \underbrace{b,\ldots,b}_{\text{l b^,s}}\hspace{10} \large\underbrace{\overbrace{a\ldots a}^{\text{k a^,s}}, \overbrace{b\ldots b}^{\text{l b^,s}}}_{\text{k+l elements}}
    [/tex]

    -cvj

  28. Clifford says:

    [tex]\normalsize \left(\large\begin{array}{GC+23} \varepsilon_x\\\varepsilon_y\\\varepsilon_z\\\gamma_{xy}\\ \gamma_{xz}\\\gamma_{yz}\end{array}\right)\ {\Large=} \ \left[\begin{array}{CC} \begin{array}\frac1{E_{\fs{+1}x}} & -\frac{\nu_{xy}}{E_{\fs{+1}x}} &-\frac{\nu_{\fs{+1}xz}}{E_{\fs{+1}x}}\\ -\frac{\nu_{yx}}{E_y}&\frac1{E_{y}}&-\frac{\nu_{yz}}{E_y}\\ -\frac{\nu_{\fs{+1}zx}}{E_{\fs{+1}z}}& -\frac{\nu_{zy}}{E_{\fs{+1}z}} &\frac1{E_{\fs{+1}z}}\end{array} & {\LARGE 0} \\ {\LARGE 0} & \begin{array}\frac1{G_{xy}}&&\\ &\frac1{G_{\fs{+1}xz}}&\\&&\frac1{G_{yz}}\end{array} \end{array}\right] \ \left(\large\begin{array} \sigma_x\\\sigma_y\\\sigma_z\\\tau_{xy}\\\tau_{xz}\\\tau_{yz} \end{array}\right)[/tex]

    -cvj

  29. Clifford says:

    Yes…. I got carried away and tried to see how these look. I borrowed these examples from the mimetex site.

    (Had to use the html ampersand character code for the ampersand column delimiter in the array function, ironically.)

    Too much fun.

    -cvj

  30. Clifford says:

    [tex]\Large\hspace{5}\unitlength{1} \picture(175,100){~(50,50){\circle(100)} (1,50){\overbrace{\line(46)}^{4$\;\;a}} (52,50){\line(125)}~(50,52;115;2){\mid}~(52,55){\longleftar[60]} (130,56){\longrightar[35]}~(116,58){r}~(c85,50;80;2){\bullet} (c85,36){3$-q}~(c165,36){3$q} (42,29){\underbrace{\line(32)}_{1$a^2/r\;\;\;}}~}[/tex]

    -cvj

  31. damtp_dweller says:

    Can you use the [ itex ] tag to put tex inline? Like [itex]\overline{R}=\phi^{-4}(R-8\phi^{-1}\Delta\phi)[/itex]? That should be an inline version of the Lichnerowicz equation.

    [tex]Y[g] \equiv \stackrel{\mathrm{inf}}{\theta\in\mathcal{F}(\mathcal{M})}\frac{\int d^3x \,\sqrt{g}((\nabla\theta)^2 + \frac{1}{8}R\theta^2)}{\left(\int d^3x \,\sqrt{g}\theta^6\right)^{1/3}}.[/tex]

  32. damtp_dweller says:

    Apparently not. πŸ™‚

  33. Aaron F. says:

    damtp_dweller — If you want inline equations, you should just be able to stick whatever the [tex]\int \, f(u) \; dk[\tex] you want right into the flow of text. Let’s find out…

  34. Aaron F. says:

    Damn! I misbackslashed! As I was saying, if you want inline equations, you should just be able to stick whatever the [tex]\int \, f(u) \; dk[/tex] you want right into the flow of text. Fingers crossed…

  35. Aaron F. says:

    Not perfect, but it doesn’t break the flow of text too much!. Also, it looks like spacing works much better in the integrals than it did with the set stuff. Let’s try that again without the \, after the integral, and with a normal \, instead of a \; before the dk…

    As you can see, we may replace the blah blah with fufufufu in equation whatnot, allowing us to generate several lines of dummy text merely to ascertain the effects of [tex]\int f(u) \, dk[/tex] on vertical spacing, as well as to experiment with internal spacing parameters on [tex]\LaTeX[/tex] output.

  36. Hmm says:

    [tex] {\cal M}(s,t,u) = -g_s^2 K \frac{\Gamma[-s] \Gamma[-t] \Gamma[-u]}{\Gamma[1 + s] \Gamma[1 + t] \Gamma[1 + u]}[/tex]

  37. Hmm says:

    Awesome. Or rather,
    [tex] \int d^4 \theta \Sum_j \phi_j^\dagger e^{2 V \cdot T_j} \phi_j + \int d^2 \theta \tau {\cal W}_\alpha {\cal W}^\alpha + \int d^2 \theta W(\phi) + \rm{h.c.}[/tex]
    awesome!

  38. Lubos Motl says:

    “Just finished assigning grades for my course and so I am oozing with good will.”

    This is what I would call the ultimate [tex] \mathcal{FREEDOM} [/tex] of expression – I would if I had two chances. πŸ™‚

  39. Clifford says:

    Ok, but that’s it. I’m not having you start abusing people, etc.

    -cvj

  40. It will be interesting to see whether people find this usable.

    I’m pretty bad at composing error-free TeX without benefit of a preview.

  41. Clifford says:

    Well we shall see. If people find it useful for even simple formulae in making their point, it will have been useful. People also might use it to drop in an equation from another source, such as a paper under discussion, etc., which can then be more easily pointed to. I will also be able to use it for longer posts.

    -cvj

  42. Carl Brannen says:

    Pictures! No way!

    \setlength{\unitlength}{1.0pt}
    \begin{picture}(235,170)
    \thinlines
    \put(35,30){\vector(1,0){113}}
    \put( 40,27){\line(0,1){6}}
    \put( 90,27){\line(0,1){6}}
    \put(140,27){\line(0,1){6}}
    \put( 25,15){$-0.5$}
    \put( 85,15){$0.0$}
    \put(135,15){$0.5$}
    \put(120,8){$t_3$}
    \put(30,35){\vector(0,1){133}}
    \put(27, 40){\line(1,0){6}}
    \put(27, 70){\line(1,0){6}}
    \put(27,100){\line(1,0){6}}
    \put(27,130){\line(1,0){6}}
    \put(27,160){\line(1,0){6}}
    \put(10, 40){-1.0}
    \put(10, 70){-0.5}
    \put(10,100){ 0.0}
    \put(10,130){ 0.5}
    \put(10,160){ 1.0}
    \put( 5,150){$t_0$}
    \thinlines
    \put( 40,130){\line(0,-1){60}}
    \put( 90,100){\line(0,-1){60}}
    \put(140,130){\line(0,-1){60}}
    \put( 40, 70){\line(5,-3){50}}
    \put( 40,130){\line(5,-3){50}}
    \put( 90,160){\line(5,-3){50}}
    \put( 90, 40){\line(5, 3){50}}
    \put( 90,100){\line(5, 3){50}}
    \put( 40,130){\line(5, 3){50}}
    \put(205,100){\vector(0,-1){30}} \put(195, 70){$n$}
    \put(205,100){\vector(3, 2){25}} \put(235,115){$l$}
    \put(205,100){\vector(-3,2){25}} \put(170,116){$m$}
    \put( 40, 70){\circle*{3}}
    \put( 40, 90){\circle*{3}}
    \put( 40,110){\circle*{3}}
    \put( 40,130){\circle*{3}}
    \put( 90, 40){\circle*{3}}
    \put( 90, 60){\circle*{3}}
    \put( 90, 80){\circle*{3}}
    \put( 90,100){\circle*{3}}
    \put( 90,120){\circle{3}}
    \put( 90,140){\circle{3}}
    \put( 90,160){\circle*{3}}
    \put(140, 70){\circle*{3}}
    \put(140, 90){\circle*{3}}
    \put(140,110){\circle*{3}}
    \put(140,130){\circle*{3}}
    \put( 45, 70){$e_L $}
    \put( 45, 90){$\bar{u}_{*R}$}
    \put( 45,110){$d_{*L} $}
    \put( 50,128){$\bar{\nu}_R $}
    \put( 95, 38){$e_R $}
    \put( 95, 55){$\bar{u}_{*L}$}
    \put( 95, 75){$d_{*R} $}
    \put( 95, 95){$\bar{\nu}_L $}
    \put( 95,115){$\bar{d}_{*L}$}
    \put( 95,135){$u_{*R} $}
    \put( 98,159){$\bar{e}_L $}
    \put(145, 70){$\nu_L $}
    \put(145, 90){$\bar{d}_{*R}$}
    \put(145,110){$u_{*L} $}
    \put(145,130){$\bar{e}_R $}
    \end{picture}

    (weak hypercharge and weak isospin for 1st generation)

  43. Carl Brannen says:

    Ouch. Delete that.

    [tex]
    \setlength{\unitlength}{1.0pt}
    \begin{picture}(235,170)
    \thinlines
    \put(35,30){\vector(1,0){113}}
    \put( 40,27){\line(0,1){6}}
    \put( 90,27){\line(0,1){6}}
    \put(140,27){\line(0,1){6}}
    \put( 25,15){$-0.5$}
    \put( 85,15){$0.0$}
    \put(135,15){$0.5$}
    \put(120,8){$t_3$}
    \put(30,35){\vector(0,1){133}}
    \put(27, 40){\line(1,0){6}}
    \put(27, 70){\line(1,0){6}}
    \put(27,100){\line(1,0){6}}
    \put(27,130){\line(1,0){6}}
    \put(27,160){\line(1,0){6}}
    \put(10, 40){-1.0}
    \put(10, 70){-0.5}
    \put(10,100){ 0.0}
    \put(10,130){ 0.5}
    \put(10,160){ 1.0}
    \put( 5,150){$t_0$}
    \thinlines
    \put( 40,130){\line(0,-1){60}}
    \put( 90,100){\line(0,-1){60}}
    \put(140,130){\line(0,-1){60}}
    \put( 40, 70){\line(5,-3){50}}
    \put( 40,130){\line(5,-3){50}}
    \put( 90,160){\line(5,-3){50}}
    \put( 90, 40){\line(5, 3){50}}
    \put( 90,100){\line(5, 3){50}}
    \put( 40,130){\line(5, 3){50}}
    \put(205,100){\vector(0,-1){30}} \put(195, 70){$n$}
    \put(205,100){\vector(3, 2){25}} \put(235,115){$l$}
    \put(205,100){\vector(-3,2){25}} \put(170,116){$m$}
    \put( 40, 70){\circle*{3}}
    \put( 40, 90){\circle*{3}}
    \put( 40,110){\circle*{3}}
    \put( 40,130){\circle*{3}}
    \put( 90, 40){\circle*{3}}
    \put( 90, 60){\circle*{3}}
    \put( 90, 80){\circle*{3}}
    \put( 90,100){\circle*{3}}
    \put( 90,120){\circle{3}}
    \put( 90,140){\circle{3}}
    \put( 90,160){\circle*{3}}
    \put(140, 70){\circle*{3}}
    \put(140, 90){\circle*{3}}
    \put(140,110){\circle*{3}}
    \put(140,130){\circle*{3}}
    \put( 45, 70){$e_L $}
    \put( 45, 90){$\bar{u}_{*R}$}
    \put( 45,110){$d_{*L} $}
    \put( 50,128){$\bar{\nu}_R $}
    \put( 95, 38){$e_R $}
    \put( 95, 55){$\bar{u}_{*L}$}
    \put( 95, 75){$d_{*R} $}
    \put( 95, 95){$\bar{\nu}_L $}
    \put( 95,115){$\bar{d}_{*L}$}
    \put( 95,135){$u_{*R} $}
    \put( 98,159){$\bar{e}_L $}
    \put(145, 70){$\nu_L $}
    \put(145, 90){$\bar{d}_{*R}$}
    \put(145,110){$u_{*L} $}
    \put(145,130){$\bar{e}_R $}
    \end{picture}
    [/tex]

    (weak hypercharge and weak isospin for 1st generation)

  44. Aaron Bergman says:

    Hmmmm. I wonder what plugins are available:

    [tex]\xymatrix{
    {} (0,1)} \ar@2{->}[]-/u 4mm/*{\bullet};[dr]-/r
    8mm/*{\bullet}^{b_j} \\
    {\mathcal{O}} \ar@2{->}[]-/l 4mm/*{\bullet};[ur]-/u 4mm/^{a_i} (1,1)} \ar@2{->}[]-/r 8mm/*{\bullet};
    [dl]-/d 4mm/*{\bullet}^{c_k} \\
    {} (1,2)} \ar@2{->}[]-/d 4mm/;[ul]-/l 4mm/^{d_l} }}[/tex]

  45. Carl Brannen says:

    Hmmm.

    [tex]
    \Large\hspace\unitlength{1}
    \begin{picture}(235,170)
    \thinlines
    \put(35,30){\vector(1,0){113}}
    \put( 40,27){\line(0,1){6}}
    \put( 90,27){\line(0,1){6}}
    \put(140,27){\line(0,1){6}}
    \put( 25,15){$-0.5$}
    \put( 85,15){$0.0$}
    \put(135,15){$0.5$}
    \put(120,8){$t_3$}
    \put(30,35){\vector(0,1){133}}
    \put(27, 40){\line(1,0){6}}
    \put(27, 70){\line(1,0){6}}
    \put(27,100){\line(1,0){6}}
    \put(27,130){\line(1,0){6}}
    \put(27,160){\line(1,0){6}}
    \put(10, 40){-1.0}
    \put(10, 70){-0.5}
    \put(10,100){ 0.0}
    \put(10,130){ 0.5}
    \put(10,160){ 1.0}
    \put( 5,150){$t_0$}
    \thinlines
    \put( 40,130){\line(0,-1){60}}
    \put( 90,100){\line(0,-1){60}}
    \put(140,130){\line(0,-1){60}}
    \put( 40, 70){\line(5,-3){50}}
    \put( 40,130){\line(5,-3){50}}
    \put( 90,160){\line(5,-3){50}}
    \put( 90, 40){\line(5, 3){50}}
    \put( 90,100){\line(5, 3){50}}
    \put( 40,130){\line(5, 3){50}}
    \put(205,100){\vector(0,-1){30}} \put(195, 70){$n$}
    \put(205,100){\vector(3, 2){25}} \put(235,115){$l$}
    \put(205,100){\vector(-3,2){25}} \put(170,116){$m$}
    \put( 40, 70){\circle*{3}}
    \put( 40, 90){\circle*{3}}
    \put( 40,110){\circle*{3}}
    \put( 40,130){\circle*{3}}
    \put( 90, 40){\circle*{3}}
    \put( 90, 60){\circle*{3}}
    \put( 90, 80){\circle*{3}}
    \put( 90,100){\circle*{3}}
    \put( 90,120){\circle{3}}
    \put( 90,140){\circle{3}}
    \put( 90,160){\circle*{3}}
    \put(140, 70){\circle*{3}}
    \put(140, 90){\circle*{3}}
    \put(140,110){\circle*{3}}
    \put(140,130){\circle*{3}}
    \put( 45, 70){$e_L $}
    \put( 45, 90){$\bar{u}_{*R}$}
    \put( 45,110){$d_{*L} $}
    \put( 50,128){$\bar{\nu}_R $}
    \put( 95, 38){$e_R $}
    \put( 95, 55){$\bar{u}_{*L}$}
    \put( 95, 75){$d_{*R} $}
    \put( 95, 95){$\bar{\nu}_L $}
    \put( 95,115){$\bar{d}_{*L}$}
    \put( 95,135){$u_{*R} $}
    \put( 98,159){$\bar{e}_L $}
    \put(145, 70){$\nu_L $}
    \put(145, 90){$\bar{d}_{*R}$}
    \put(145,110){$u_{*L} $}
    \put(145,130){$\bar{e}_R $}
    \end{picture}
    [/tex]

  46. Aaron Bergman says:

    Does usepackage work?

    [tex]
    \usepackage{xypic}
    \xymatrix{
    {} (0,1)} \ar@2{->}[]-/u 4mm/*{\bullet};[dr]-/r
    8mm/*{\bullet}^{b_j} \\
    {\mathcal{O}} \ar@2{->}[]-/l 4mm/*{\bullet};[ur]-/u 4mm/^{a_i} (1,1)} \ar@2{->}[]-/r 8mm/*{\bullet};
    [dl]-/d 4mm/*{\bullet}^{c_k} \\
    {} (1,2)} \ar@2{->}[]-/d 4mm/;[ul]-/l 4mm/^{d_l} }}
    [/tex]

    (If this doesn’t work, that’s it for me)

  47. Carl Brannen says:

    Test scaling:

    [tex]
    \Large\hspace\unitlength{1}
    \begin{picture}(470,340)
    \thinlines
    \put(70,60){\vector(1,0){113}}
    \put( 80,54){\line(0,1){6}}
    \put(180,54){\line(0,1){6}}
    \put(280,54){\line(0,1){6}}
    \put(100,30){$-0.5$}
    \put(170,30){$0.0$}
    \put(270,30){$0.5$}
    \put(240,16){$t_3$}
    \put(60,70){\vector(0,1){133}}
    \put(54, 80){\line(1,0){6}}
    \put(54,140){\line(1,0){6}}
    \put(54,200){\line(1,0){6}}
    \put(54,260){\line(1,0){6}}
    \put(54,320){\line(1,0){6}}
    \put(20, 80){-1.0}
    \put(20,140){-0.5}
    \put(20,200){ 0.0}
    \put(20,260){ 0.5}
    \put(20,320){ 1.0}
    \put(10,300){$t_0$}
    \thinlines
    \put( 80,260){\line(0,-1){60}}
    \put(180,200){\line(0,-1){60}}
    \put(280,260){\line(0,-1){60}}
    \put( 80,140){\line(5,-3){50}}
    \put( 80,260){\line(5,-3){50}}
    \put(180,320){\line(5,-3){50}}
    \put(180, 80){\line(5, 3){50}}
    \put(180,200){\line(5, 3){50}}
    \put( 80,260){\line(5, 3){50}}
    \end{picture}
    [/tex]

  48. Carl Brannen says:

    I wonder how many tests I can screw up before I get banned?

    [tex]
    \Large\hspace\unitlength{1}
    \begin{picture}(470,340)
    \thinlines
    \put(70,60){\line(1,0){226}}
    \put( 80,54){\line(0,1){12}}
    \put(180,54){\line(0,1){12}}
    \put(280,54){\line(0,1){12}}
    \put(100,30){$-0.5$}
    \put(170,30){$0.0$}
    \put(270,30){$0.5$}
    \put(240,16){$t_3$}
    \put(60,70){\line(0,1){266}}
    \put(54, 80){\line(1,0){12}}
    \put(54,140){\line(1,0){12}}
    \put(54,200){\line(1,0){12}}
    \put(54,260){\line(1,0){12}}
    \put(54,320){\line(1,0){12}}
    \put(20, 80){-1.0}
    \put(20,140){-0.5}
    \put(20,200){ 0.0}
    \put(20,260){ 0.5}
    \put(20,320){ 1.0}
    \put(10,300){$t_0$}
    \thinlines
    \put( 80,140){\line(0,1){120}}
    \put(180, 80){\line(0,1){120}}
    \put(280,140){\line(0,1){120}}
    \put( 80,140){\line(5,-3){100}}
    \put( 80,260){\line(5,-3){100}}
    \put(180,320){\line(5,-3){100}}
    \put(180, 80){\line(5, 3){100}}
    \put(180,200){\line(5, 3){100}}
    \put( 80,260){\line(5, 3){100}}
    \put(410,200){\vector(0,-1){30}} \put(390,140){$n$}
    \put(410,200){\vector(3, 2){25}} \put(470,230){$l$}
    \put(410,200){\vector(-3,2){25}} \put(340,232){$m$}
    \put( 80,140){\circle*{3}}
    \put( 80,180){\circle*{3}}
    \put( 80,220){\circle*{3}}
    \put( 80,260){\circle*{3}}
    \put(180, 80){\circle*{3}}
    \put(180,120){\circle*{3}}
    \put(180,160){\circle*{3}}
    \put(180,200){\circle*{3}}
    \put(180,240){\circle{3}}
    \put(180,280){\circle{3}}
    \put(180,320){\circle*{3}}
    \put(280,140){\circle*{3}}
    \put(280,180){\circle*{3}}
    \put(280,220){\circle*{3}}
    \put(280,260){\circle*{3}}
    \put( 90,140){$e_L $}
    \put( 90,180){$\bar{u}_{*R}$}
    \put( 90,220){$d_{*L} $}
    \put( 50,128){$\bar{\nu}_R $}
    \put(190, 76){$e_R $}
    \put(190,110){$\bar{u}_{*L}$}
    \put(190,150){$d_{*R} $}
    \put(190,190){$\bar{\nu}_L $}
    \put(190,230){$\bar{d}_{*L}$}
    \put(190,270){$u_{*R} $}
    \put(196,318){$\bar{e}_L $}
    \put(290,140){$\nu_L $}
    \put(290,180){$\bar{d}_{*R}$}
    \put(290,220){$u_{*L} $}
    \put(290,260){$\bar{e}_R $}
    \end{picture}
    [/tex]

  49. Clifford, you mentioned your private research blog. Maybe I live in a cave or something, but I’ve never heard of that idea; it sounds like a great one though. Can I ask you to post or comment on how it works? (How it’s structured, pro’s and con’s, etc.)

  50. jay says:

    just a test
    [tex]\int\ \Gamma(x) dx [/tex]

  51. Carl Brannen says:

    [tex]
    \Large\hspace\unitlength{1}
    \begin{picture}(470,340)
    \put(70,60){\line(1,0){226}}
    \put( 80,54){\line(0,1){12}}
    \put(180,54){\line(0,1){12}}
    \put(280,54){\line(0,1){12}}
    \put(100,30){$-0.5$}
    \put(170,30){$0.0$}
    \put(270,30){$0.5$}
    \put(240,16){$t_3$}
    \put(60,70){\line(0,1){266}}
    \put(54, 80){\line(1,0){12}}
    \put(54,140){\line(1,0){12}}
    \put(54,200){\line(1,0){12}}
    \put(54,260){\line(1,0){12}}
    \put(54,320){\line(1,0){12}}
    \put(20, 80){-1.0}
    \put(20,140){-0.5}
    \put(20,200){ 0.0}
    \put(20,260){ 0.5}
    \put(20,320){ 1.0}
    \put(10,300){$t_0$}
    \put( 80,140){\line(0,1){120}}
    \put(180, 80){\line(0,1){120}}
    \put(280,140){\line(0,1){120}}
    \put( 80,140){\line(5,-3){100}}
    \put( 80,260){\line(5,-3){100}}
    \put(180,320){\line(5,-3){100}}
    \put(180, 80){\line(5, 3){100}}
    \put(180,200){\line(5, 3){100}}
    \put( 80,260){\line(5, 3){100}}
    \put( 80,140){\circle*{15}}
    \put( 80,180){\circle*{15}}
    \put( 80,220){\circle*{15}}
    \put( 80,260){\circle*{15}}
    \put(180, 80){\circle*{15}}
    \put(180,120){\circle*{15}}
    \put(180,160){\circle*{15}}
    \put(180,200){\circle*{15}}
    \put(180,240){\circle{15}}
    \put(180,280){\circle{15}}
    \put(180,320){\circle*{15}}
    \put(280,140){\circle*{15}}
    \put(280,180){\circle*{15}}
    \put(280,220){\circle*{15}}
    \put(280,260){\circle*{15}}
    \put( 90,140){$e_L $}
    \put( 90,180){$\bar{u}_{*R}$}
    \put( 90,220){$d_{*L} $}
    \put( 50,128){$\bar{\nu}_R $}
    \put(190, 76){$e_R $}
    \put(190,110){$\bar{u}_{*L}$}
    \put(190,150){$d_{*R} $}
    \put(190,190){$\bar{\nu}_L $}
    \put(190,230){$\bar{d}_{*L}$}
    \put(190,270){$u_{*R} $}
    \put(196,318){$\bar{e}_L $}
    \put(290,140){$\nu_L $}
    \put(290,180){$\bar{d}_{*R}$}
    \put(290,220){$u_{*L} $}
    \put(290,260){$\bar{e}_R $}
    \end{picture}
    [/tex]

  52. Carl Brannen says:

    Okay. I couldn’t get \circle or \vector to work. Scaling was awful. And vertical lines (i.e. “\put( 80,140){\line(0,1){120}}” didn’t work either. How about qbezier?

    [tex]
    \Large\hspace\unitlength{1}
    \begin{picture}(470,340)
    \put(70,60){\line(1,0){226}}
    \put(100,30){$-0.5$}
    \put(170,30){$0.0$}
    \put(270,30){$0.5$}
    \put(240,16){$t_3$}
    \put(60,70){\line(0,1){266}}
    \put(54, 80){\line(1,0){12}}
    \put(54,140){\line(1,0){12}}
    \put(54,200){\line(1,0){12}}
    \put(54,260){\line(1,0){12}}
    \put(54,320){\line(1,0){12}}
    \put(20, 80){-1.0}
    \put(20,140){-0.5}
    \put(20,200){ 0.0}
    \put(20,260){ 0.5}
    \put(20,320){ 1.0}
    \put(10,300){$t_0$}
    \qbezier(80,140)(80,140)(80,260)
    \qbezier(120,80)(120,80)(120,200)
    \qbezier(280,140)(280,140)(280,260)
    \put( 80,140){\line(5,-3){100}}
    \put( 80,260){\line(5,-3){100}}
    \put(180,320){\line(5,-3){100}}
    \put(180, 80){\line(5, 3){100}}
    \put(180,200){\line(5, 3){100}}
    \put( 80,260){\line(5, 3){100}}
    \put( 90,140){$e_L $}
    \put( 90,180){$\bar{u}_{*R}$}
    \put( 90,220){$d_{*L} $}
    \put( 50,128){$\bar{\nu}_R $}
    \put(190, 76){$e_R $}
    \put(190,110){$\bar{u}_{*L}$}
    \put(190,150){$d_{*R} $}
    \put(190,190){$\bar{\nu}_L $}
    \put(190,230){$\bar{d}_{*L}$}
    \put(190,270){$u_{*R} $}
    \put(196,318){$\bar{e}_L $}
    \put(290,140){$\nu_L $}
    \put(290,180){$\bar{d}_{*R}$}
    \put(290,220){$u_{*L} $}
    \put(290,260){$\bar{e}_R $}
    \end{picture}
    [/tex]

  53. Carl Brannen says:

    no qbezier. But awesome speed. I swear that Latex takes longer than this for short programs on my iNTEL laptop.

  54. Robert says:

    Warmup [tex]\int d^2\sigma\,\partial X\bar\partial X[/tex]

  55. Robert says:

    OK, let’s be a bit nasty: [tex]\input /etc/passwd[/tex]

  56. Clifford says:

    Kishan Yerubandi:- Actually, I’ve been meaning to post about that for a while now. Give me a little while longer.

    Carl Brannen, Aaron Bergmann: – The experiments are fun aren’t they? I do not know the limitations of mimetex, but I suspect that they are very severe in terms of the LaTeX things you are used to. So I do not expect that it will be able to use any TeX library packages of the sort you were trying to load, Aaron, or do a number of the picture elements that you might need Carl. But basic LaTeX allows one to do a great deal (certainly a great deal more than text in comments and posts), so this could be useful. To do proper LaTeX would require LaTeX to be running on the server, with all the whistles and bells you can get going as usual on a computer with that on. This is not what is going on here. You’d need latexrender proper for that… I’m using mimetex to bypass that since my server does not have LaTeX on it. My hosts probably are not familiar with that at all.

    Do have a look over at the sites I linked to for some of the rather clever tools they have developed though, like illustration pacakages and the like. Maybe I will see if I can put some of them on here if they look possible and useful.

    -cvj

  57. Clifford says:

    Carl Brannen: – MimeTeX user manual here. I think everyone wants to see what you final picture was suppposed to be!

    -cvj

  58. Robert says:

    again: [tex]\openout7=foo\write7{bar]\closeout7\openin7=foo\read7 to \bla\closein7\bla[/tex]

  59. Gina says:

    [tex] \frac {\bar {\Xsi}}{\Xsi}[\tex]

  60. Supernova says:

    Okay, it had to be said: You people are all a bunch of dorks. πŸ˜€

  61. Gina says:

    [tex] \frac {\bar {\Xsi}}{\Xsi}[/tex]

  62. Gina says:

    [tex] \frac {\bar {\Xi}}{\Xi}[/tex]

  63. Clifford says:

    Such happy dorks, though! πŸ™‚ πŸ˜€

    -cvj

  64. Carl Brannen says:

    It turns out that the mimetex picture drawing elements are in certain ways superior to the native commands in LaTex. Vertical lines not working is a bug that only shows up if you use a less efficient method of defining them (I hope).

    Whatever, I’m going to see if I can get them to install this over at Physics Forums, where pictures have always been an issue.

    [tex]
    \begin{picture}(470,340)
    \put( 70,60){\line(226,0)}
    \put( 80,54){\line(0,12)}
    \put(180,54){\line(0,12)}
    \put(280,54){\line(0,12)}
    \put( 50,30){$-0.5$}
    \put(170,30){$0.0$}
    \put(270,30){$0.5$}
    \put(240,16){$t_3$}
    \put(60,70){\vector(0,266)}
    \put(54, 80){\line(12,0)}
    \put(54,140){\line(12,0)}
    \put(54,200){\line(12,0)}
    \put(54,260){\line(12,0)}
    \put(54,320){\line(12,0)}
    \put(20, 80){-1.0}
    \put(20,140){-0.5}
    \put(20,200){ 0.0}
    \put(20,260){ 0.5}
    \put(20,320){ 1.0}
    \put(10,300){$t_0$}
    \put( 80,260){\line(0,-60)}
    \put(180,200){\line(0,-60)}
    \put(280,260){\line(0,-60)}
    \put( 80,140){\line(5,-3){50}}
    \put( 80,260){\line(5,-3){50}}
    \put(180,320){\line(5,-3){50}}
    \put(180, 80){\line(5, 3){50}}
    \put(180,200){\line(5, 3){50}}
    \put( 80,260){\line(5, 3){50}}
    \put( 80,140){\circle(6)}
    \put( 80,180){\circle(6)}
    \put( 80,220){\circle(6)}
    \put( 80,260){\circle(6)}
    \put(180, 80){\circle(6)}
    \put(180,120){\circle(6)}
    \put(180,160){\circle(6)}
    \put(180,200){\circle(6)}
    \put(180,240){\circle(6)}
    \put(180,280){\circle(6)}
    \put(180,320){\circle(6)}
    \put(180,140){\circle(6)}
    \put(180,180){\circle(6)}
    \put(180,220){\circle(6)}
    \put(180,260){\circle(6)}
    \put( 90,140){$e_L $}
    \put( 90,180){$\bar{u}_{*R}$}
    \put( 90,220){$d_{*L} $}
    \put(100,256){$\bar{\nu}_R $}
    \put(190, 76){$e_R $}
    \put(190,110){$\bar{u}_{*L}$}
    \put(190,150){$d_{*R} $}
    \put(190,190){$\bar{\nu}_L $}
    \put(190,230){$\bar{d}_{*L}$}
    \put(190,270){$u_{*R} $}
    \put(196,318){$\bar{e}_L $}
    \put(290,140){$\nu_L $}
    \put(290,180){$\bar{d}_{*R}$}
    \put(290,220){$u_{*L} $}
    \put(290,260){$\bar{e}_R $}
    \end{picture}
    [/tex]

    Should be elementary particles of first generation, plotted according to weak hypercharge and weak isospin.

    [Apply prayer, hit submit]

  65. Carl Brannen says:

    Easy to fix:

    [tex]
    \begin{picture}(470,340)
    \put( 70,60){\line(226,0)}
    \put( 80,54){\line(0,12)}
    \put(180,54){\line(0,12)}
    \put(280,54){\line(0,12)}
    \put( 50,30){$-0.5$}
    \put(170,30){$0.0$}
    \put(270,30){$0.5$}
    \put(240,16){$t_3$}
    \put(60,70){\line(0,266)}
    \put(54, 80){\line(12,0)}
    \put(54,140){\line(12,0)}
    \put(54,200){\line(12,0)}
    \put(54,260){\line(12,0)}
    \put(54,320){\line(12,0)}
    \put(20, 80){-1.0}
    \put(20,140){-0.5}
    \put(20,200){ 0.0}
    \put(20,260){ 0.5}
    \put(20,320){ 1.0}
    \put(10,300){$t_0$}
    \put( 80,260){\line(0,-120)}
    \put(180,200){\line(0,-120)}
    \put(280,260){\line(0,-120)}
    \put( 80,140){\line(5,-3){100}}
    \put( 80,260){\line(5,-3){100}}
    \put(180,320){\line(5,-3){100}}
    \put(180, 80){\line(5, 3){100}}
    \put(180,200){\line(5, 3){100}}
    \put( 80,260){\line(5, 3){100}}
    \put( 80,140){\circle(6)}
    \put( 80,180){\circle(6)}
    \put( 80,220){\circle(6)}
    \put( 80,260){\circle(6)}
    \put(180, 80){\circle(6)}
    \put(180,120){\circle(6)}
    \put(180,160){\circle(6)}
    \put(180,200){\circle(6)}
    \put(180,240){\circle(6)}
    \put(180,280){\circle(6)}
    \put(180,320){\circle(6)}
    \put(180,140){\circle(6)}
    \put(180,180){\circle(6)}
    \put(180,220){\circle(6)}
    \put(180,260){\circle(6)}
    \put( 90,140){$e_L $}
    \put( 90,180){$\bar{u}_{*R}$}
    \put( 90,220){$d_{*L} $}
    \put(100,256){$\bar{\nu}_R $}
    \put(190, 76){$e_R $}
    \put(190,110){$\bar{u}_{*L}$}
    \put(190,150){$d_{*R} $}
    \put(190,190){$\bar{\nu}_L $}
    \put(190,230){$\bar{d}_{*L}$}
    \put(190,270){$u_{*R} $}
    \put(196,318){$\bar{e}_L $}
    \put(290,140){$\nu_L $}
    \put(290,180){$\bar{d}_{*R}$}
    \put(290,220){$u_{*L} $}
    \put(290,260){$\bar{e}_R $}
    \end{picture}
    [/tex]

    1st generation plotted according to weak hypercharge and weak isospin. Suggestive that the antiparticles are defined rather arbitrarily, and that the structure of idempotents of Clifford algebras (hypercubes) be used to model internal symmetries.

  66. Carl Brannen says:

    Oh, that was close:

    [tex]
    \begin{picture}(470,340)
    \put( 70,60){\line(226,0)}
    \put( 80,54){\line(0,12)}
    \put(180,54){\line(0,12)}
    \put(280,54){\line(0,12)}
    \put( 50,30){$-0.5$}
    \put(170,30){$0.0$}
    \put(270,30){$0.5$}
    \put(240,16){$t_3$}
    \put(60,70){\line(0,266)}
    \put(54, 80){\line(12,0)}
    \put(54,140){\line(12,0)}
    \put(54,200){\line(12,0)}
    \put(54,260){\line(12,0)}
    \put(54,320){\line(12,0)}
    \put(20, 80){-1.0}
    \put(20,140){-0.5}
    \put(20,200){ 0.0}
    \put(20,260){ 0.5}
    \put(20,320){ 1.0}
    \put(10,300){$t_0$}
    \put( 80,260){\line(0,-120)}
    \put(180,200){\line(0,-120)}
    \put(280,260){\line(0,-120)}
    \put( 80,140){\line(5,-3){100}}
    \put( 80,260){\line(5,-3){100}}
    \put(180,320){\line(5,-3){100}}
    \put(180, 80){\line(5, 3){100}}
    \put(180,200){\line(5, 3){100}}
    \put( 80,260){\line(5, 3){100}}
    \put( 80,140){\circle(6)}
    \put( 80,180){\circle(6)}
    \put( 80,220){\circle(6)}
    \put( 80,260){\circle(6)}
    \put(180, 80){\circle(6)}
    \put(180,120){\circle(6)}
    \put(180,160){\circle(6)}
    \put(180,200){\circle(6)}
    \put(180,240){\circle(6)}
    \put(180,280){\circle(6)}
    \put(180,320){\circle(6)}
    \put(280,140){\circle(6)}
    \put(280,180){\circle(6)}
    \put(280,220){\circle(6)}
    \put(280,260){\circle(6)}
    \put( 90,140){$e_L $}
    \put( 90,180){$\bar{u}_{*R}$}
    \put( 90,220){$d_{*L} $}
    \put(100,256){$\bar{\nu}_R $}
    \put(190, 76){$e_R $}
    \put(190,110){$\bar{u}_{*L}$}
    \put(190,150){$d_{*R} $}
    \put(190,190){$\bar{\nu}_L $}
    \put(190,230){$\bar{d}_{*L}$}
    \put(190,270){$u_{*R} $}
    \put(196,318){$\bar{e}_L $}
    \put(290,140){$\nu_L $}
    \put(290,180){$\bar{d}_{*R}$}
    \put(290,220){$u_{*L} $}
    \put(290,260){$\bar{e}_R $}
    \end{picture}
    [/tex]

  67. Carl Brannen says:

    The picture drawing is superior to the LaTex standard \xypic in that the line draws are not limited to small integer ratios. To get around that in \xypic, one uses the qbezier, which draws nice curves.

    I gotta have this.

  68. Clifford says:

    Excellent! Happy to have provided information about a new and useful tool…!

    -cvj

  69. Thomas Larsson says:

    This reminds me of when Peter introduced Latexrender.

  70. Warren says:

    In case you missed it, the LaTeÏ‑ code appears when your mouse hovers over the figure.

  71. Warren says:

    Any way to get the fonts less jaggy?

  72. Warren says:

    Just out of curiosity, let’s see how your 1st equation compares to
    uR²-½RR”+¼(R’)²=ΓŽβ€œΓ‚Β²

  73. Pingback: The n-Category Café

  74. Warren says:

    latexrender & textogif seem to produce prettier results.

  75. Navneeth says:

    [tex]\lim_{x\rightarrow\infty} \left(f(x)-\left(mx+b\right)\right) = 0[/tex]

    Getting excited over a typeset; we are certainly a bunch of geeks!

  76. I see. If you want alot of hits on your web site, give people crack. My site has CGI that creates printable add/subtract and multiply problems. Not as sexy as LaTeX. Perhaps i should look into this to create formatted divides.

  77. Anon says:

    To Carl:

    Hurrah! I have been watching your efforts with baited breath. A bit like watching a trapeze artist!

  78. Cynthia says:

    It’s truly a pleasure watching all of you folks having loads of fun performing mathematical esoterica via LaTeX. But, Clifford, please don’t let LaTeX take over Asymptotia, in its entirety! Otherwise, I–like so many mathematical zeros–will become shut out from posting on all now and future comment threads:(…

  79. Clifford says:

    Cynthia:- There are, as I write, 239 posts and 2,609 comments on the blog. Only one post is about LaTeX (or so far even has it) and only 80 comments about it (81 once I hit “Submit”). I think you’re safe (and you are not a mathematical zero, by the way).

    LaTeX is here as a tool, not a subject in and of itself.

    Besides, you can have fun with it by either watching the antics (see comment number 79), or joining in yourself and learning how to make interesting shapes and symbols appear. Think of it as a special smoking lounge I’ve set up in the house (see the living room analogy on the About page) where people can have fun blowing very exotic smoke rings. You don’t have to go into that lounge if you don’t want to, of course.

    -cvj

  80. Cynthia says:

    Clifford, thanks for the invitation to the LaTeX Matrix! When I get up the nerve, I’ll join in.;)

  81. Amara says:

    Given what I see above, this should work:
    [tex]$I_{moving}={{4\pi a^2n_i\sqrt {\left( {{{kT_i} \over {2\pi m_i}}} \right)}} \over 2}\left\{ \matrix{\left( {M^2+{1 \over 2}-\psi _i} \right)\sqrt {{\pi \over M}}\left[ {\rm erf\left( {M+\sqrt {\psi _i}} \right)+{\rm erf}\left( {M-\sqrt {\psi _i}} \right)} \right]\hfill\cr +\left( {\sqrt {{{\psi _i} \over M}}+1} \right)\exp \left[ {-\left( {M-\sqrt {\psi _i}} \right)^2} \right]\hfill\cr -\left( {\sqrt {{{\psi _i} \over M}}-1} \right)\exp \left[ {-\left( {M+\sqrt {\psi _i}} \right)^2} \right]\hfill\cr} \right\}$[/tex]

  82. Clifford says:

    It did, but the system shrunk it a bit and it looks too compressed. You can see that the full gif image is much nicer. Click here.

    -cvj

  83. Amara says:

    Way cool! Let’s look at some partial derivatives… We want to find points near a circle, so then to minimize [tex]$Q(x_c,y_c,R)=\sum_{i=1}^N\left[(x_i-x_c)^2+(y_i-y_c)^2-R^2\right]^2\,.$[/tex]. Our partial derivatives are: [tex]$\frac{\partial Q}{\partial x_c} = -4\sum_{i=1}^N \left[(x_i)-x_c)^2+(y_i-y_c)^2-R^2\right](x_i-x_c)=0\,,$[[/tex] and [tex]$\frac{\partial Q}{\partial y_c} = -4\sum_{i=1}^N \left[(x_i)-x_c)^2+(y_i-y_c)^2-R^2\right](y_i-y_c)=0\,,$[/tex] and [tex]$\frac{\partial Q}{\partial R} = -4R\sum_{i=1}^N \left[(x_i)-x_c)^2+(y_i-y_c)^2-R^2\right]=0\,.$[/tex]. From which [tex]$R^2=\frac{1}{N}\sum_{i=1}^N\left[(x_i-x_c)^2+(y_i-y_c)^2\right]\,,$[/tex].
    The answer is here:
    [tex]$\sum_{i=1}^Nx_i\left[(x_i-x_c)^2+(y_i-y_c)^2\right] =\frac{1}{N}\left(\sum_{i=1}^Nx_i\right) \sum_{i=1}^N\left[(x_i-x_c)^2+(y_i-y_c)^2\right]\,,$[/tex],
    [tex]$\sum_{i=1}^Ny_i\left[(x_i-x_c)^2+(y_i-y_c)^2\right] =\frac{1}{N}\left(\sum_{i=1}^Ny_i\right) \sum_{i=1}^N\left[(x_i-x_c)^2+(y_i-y_c)^2\right]\,.$[/tex]
    I hope it looks pretty…

  84. Amara says:

    OK, looks a bit confused. My inline equations should have been on separate lines.

  85. Clifford says:

    You don’t need the dollar signs.

    -cvj

  86. Amara says:

    Oh! I used the dollar signs in earlier example above, however. Trying again without.
    Problem: given a set of N points [tex](x_1,y_1), (x_N,y_N)[/tex] lying on a plane, find a circle which is closest to these points.
    Minimize:
    [tex]Q(x_c,y_c,R)=\sum_{i=1}^N\left[(x_i-x_c)^2+(y_i-y_c)^2-R^2\right]^2[/tex]
    For derivatives of Q, we obtain:
    [tex]\frac{\partial Q}{\partial x_c} = -4\sum_{i=1}^N\left[(x_i)-x_c)^2+(y_i-y_c)^2-R^2\right](x_i-x_c)=0[/tex]
    [tex]\frac{\partial Q}{\partial y_c} = -4\sum_{i=1}^N\left[(x_i)-x_c)^2+(y_i-y_c)^2-R^2\right](y_i-y_c)=0[/tex]
    [tex]\frac{\partial Q}{\partial R} = -4R\sum_{i=1}^N\left[(x_i)-x_c)^2+(y_i-y_c)^2-R^2\right]=0[/tex]
    From the last equation we obtain
    [tex]R^2=\frac{1}{N}\sum_{i=1}^N\left[(x_i-x_c)^2+(y_i-y_c)^2\right][/tex]
    and then:
    [tex]\sum_{i=1}^Nx_i\left[(x_i-x_c)^2+(y_i-y_c)^2\right] =\frac{1}{N}\left(\sum_{i=1}^Nx_i\right) \sum_{i=1}^N\left[(x_i-x_c)^2+(y_i-y_c)^2\right][/tex]
    [tex]\sum_{i=1}^Ny_i\left[(x_i-x_c)^2+(y_i-y_c)^2\right] =\frac{1}{N}\left(\sum_{i=1}^Ny_i\right) \sum_{i=1}^N\left[(x_i-x_c)^2+(y_i-y_c)^2\right][/tex]
    so let’s see..

  87. Plato says:

    Clifford,

    Layman question trying to transfer image to latex?

    I used to use pre and /pre to display keyboard image construction, but I was wondering seeing Carl’s diagram if such as image as the Clebsch’s Diagonal Surface can be written using that software? Simplified, or even if you wanted too?

    x^3+y^3+z^3+w^3 – (x+y+0.5z+0.5w)^3 – (0.5z+0.5w)^3

    or here…

    f(x,y,z) = x2+y2+z2-42 = 0,

    i.e. the set of all complex x,y,z satisfying the equation. What happens at the complex point (x,i*y,i*z) for some real (x,y,z)?

    f(i*x,y,z) = x2+(i*y)2+(i*z)2-42
    = x2+i2*y2+i2*z2-42
    = x2-y2-z2-42.

  88. Plato says:

    \Large\left.\begin{eqnarray} x+y+z&=&3\\2y&=&x+z\\2x+y&=&z\end{eqnarray}\right\}

  89. Plato says:

    [tex]\Large\left.\begin{eqnarray} x+y+z&=&3\\2y&=&x+z\\2x+y&=&z\end{eqnarray}\right\}[/tex]

  90. stevem says:

    Should have a go:

    [tex]\int~Tr(F\wedge~F_{*})[\tex]

  91. Plato says:

    #89 in latex?

    [tex]f(x,y,z) = x2+y2+z2-42 = 0[/tex]

    i.e. the set of all complex x,y,z satisfying the equation. What happens at the complex point ([tex]x,i*y,i*z[/tex]) for some real ([tex]x,y,z[/tex])?

    [tex]f(i*x,y,z) = x2+(i*y)2+(i*z)2-42
    = x2+i2*y2+i2*z2-42
    = x2-y2-z2-42.[/tex]

  92. stevem says:

    Try again

    [ tex ]\int~Tr(F\wedge~F_{*}[ / tex]

  93. Clifford says:

    Remove the spaces in the large brackets.

    -cvj

  94. Plato says:

    oops

    first part anyway

    [tex]f(x)=/int_{-\infty}^x e^{-t^2}dt[/tex]

  95. stevem says:

    What am I doing wrong?

  96. stevem says:

    [tex]\int~Tr(F\wedge~F_{*})[/tex]

  97. stevem says:

    Let [tex]\mathbb{G}[/tex] be a simple compact Lie group and let [tex]\mathcal{R}[/tex] be a representation of [tex]\mathbb{G}[/tex]. In (3+1) and (2+1) dimensions, pure gauge theory with connection A, curvature

    [tex]F=dA+A\wedge~A[/tex]

    and Lagrangian

    [tex]\int~Tr(F\wedge_{*}F)[/tex]

    exhibits confinement.

  98. Plato says:

    [tex]f(x)=\int_{-\infty}^x e^{-t^2}dt[/tex] ex. on tutorial sorry. I was somehow thinking that the coordinates of post 89 could have been assigned a latex language other then what is seen in equation form.

  99. stevem says:

    Darn, my hodge star is out. Quite nice! Just needs a bit more practice for use in comments. The case [tex]\mathbb{G}=SU(3)[/tex] is really hard to prove though–took me hours one night πŸ™‚

  100. Kea says:

    WOW!!! Let me have a go. This is a real long shot:

    [tex]\xymatrix {A \ar[d]_{!} \ar@{{}*!/-8pt/@{>}->}[r]^{m} & B \ar[d]^{\chi_{m}} \\ 1 \ar@{{}*!/-8pt/@{>}->}[r]_{t} \Omega}[/tex]

  101. Kea says:

    OK, that was too ambitious. Sigh. But THANKS, Clifford! Is there a free blogging setup where one could do this? Or maybe we should just ask Google nicely…

  102. Euler says:

    [tex]e^{i\pi}+1=0[/tex]

  103. Garrett Lisi says:

    Hmm, how about some little arrows…
    [tex]
    {\cal L}_{\vec{v}} \underrightarrow{f} = \left( \underrightarrow{\partial} \vec{v} \right) \underrightarrow{f} + \left( \vec{v} \underrightarrow{\partial} \right) \underrightarrow{f}
    [/tex]

  104. Robert says:

    [tex]\begin{equation*}
    |x|=
    \begin{cases} x & \text{if $xÒ‰Β₯0$,}
    \\
    -x &\text{if $x\le 0$.}
    \end{cases}
    \end{equation*}[/tex]
    That’s just plain geekalicious!

  105. Garrett Lisi says:

    OK, lets try again…

    [tex]
    {\cal L}_{\overset{\rightharpoonup}{v}} \underset{\rightharpoondown}{f} = \left( \underset{\rightharpoondown}{\partial} \overset{\rightharpoonup}{v} \right) \underset{\rightharpoondown}{f} + \left( \overset{\rightharpoonup}{v} \underset{\rightharpoondown}{\partial} \right) \underset{\rightharpoondown}{f}
    [/tex]

    (By the way, that’s the Lie derivative of a 1-form.)

  106. Gebar says:

    Yes, this is really fun! And I have good news for people with blogs in Blogger or in servers that do not support latex. Have a look here. Peter Jipsen of Chapman University has written ASCIIMathML a great javascript program that converts ASCII notation (more or less the one used in math and physics newsgroups, and of course in blogs, although not this one any more:-)) to MathML. Firefox rendering is great, although you may need to download some fonts. IE needs a plugin and rendering is not so good. Now, you are supposed to upload the javascript file to your server, but I suspect that it will work also if you put the content of the file in the head of your Blogger template. (Be warned though that the file is 42K, and that I have not tried this, I just assume it will work.)

    If you do not want to risk this, there are two more solutions mentioned in the page given above. The first one are the ASCIIMath Image Fallback Scripts which use a public mimetex server (meaning you do not have to have mimetex in your server), and the second is LaTeXMathML, which as you may have guessed translates latex notation to mathml using again a public server if you cannot upload the file in your own.

    Enjoy!

  107. Carl Brannen says:

    The posts here are like the doodles that psychologists fool you into making, when they want to figure out what kind of crazy you are.

  108. Clifford says:

    Oh, I’ve got you all figured out, all of you! πŸ˜‰

    -cvj

  109. Biswajit says:

    [tex]
    \boldsymbol{\Nabla}\cdot\boldsymbol{\sigma} + \rho~\mathbf{b} = \rho~\dot{\mathbf{v}}
    [/tex]

  110. Biswajit says:

    [tex]
    \mathbf{\nabla}\cdot\mathbf{\sigma} + \rho~\mathbf{b} = \rho~\dot{\mathbf{v}}
    [\tex]

  111. Biswajit says:

    Last try. Delete immediately.
    [tex]
    \mathbf{\nabla}\cdot\mathbf{\sigma} + \rho~\mathbf{b} = \rho~\dot{\mathbf{v}}
    [/tex]

  112. Gebar says:

    OK, I did not mention the most important thing (for hardcore latex users). All the above programs (ASCIIMathML etc.) also recognize latex notation.

  113. Plato says:

    I=I_0\:{\rm e}^{-\mu x}

    Photons are attenuated in matter via the processes of the photoelectric effect, Compton scattering and pair production. The intensity of a photon beam varies in matter according to

    [tex]I=I_0\:{\rm e}^{-\mu x}[/tex]

    .

  114. Clifford says:

    fixed it for you plato. -cvj

  115. Basudeb Dasgupta says:

    The new tree knows…

    [tex] \nu_{e},\nu_{\mu},\nu_{\tau}[\tex]

  116. Basudeb Dasgupta says:

    The new tree knowsÒ€¦

    [tex] \nu_{e}, \nu_{\mu}, \nu_{\tau}[/tex]

  117. Count Iblis says:

    [tex]\exp\left(\pi\sqrt{163}\right)\approx 262537412640768743.9999999999992\ldots[/tex]

  118. Youssef Faltas says:

    [tex] T^{\mu \nu} = – \nabla^{\mu} \phi (x) \frac{\nabla L}{\nabla (\nabla_{\nu} \phi)}+ g_{\mu \nu} L\\
    \nabla_{\nu} V^{\mu} = \partial_{\nu} V^{\mu} + \Gamma^{\mu}{}_{\sigma \nu} V^{\sigma} [/tex]

  119. Plato says:

    The converse of the Principle,

    [tex]x=y \rightarrow \foral F(Fx \leftrightarrow Fy)[/tex],

    is called the Indiscernibility of Identicals. Sometimes the conjunction of both principles, rather than the Principle by itself, is known as Leibniz’s Law.

  120. Plato says:

    http://en.wikipedia.org/wiki/Perfect_fluid

    In physics, a perfect fluid is a fluid that can be completely characterized by its rest frame energy density ρ and isotropic pressure p.

    In tensor notation, the energy-momentum tensor of a perfect fluid can be written in the form

    [tex]T^{\mu\nu} = (\rho + p) \, U^\mu U^\nu + p \, \eta^{\mu\nu}\,[/tex]

    where U is the velocity vector field of the fluid and where ημν is the metric tensor of Minkowski spacetime

    How did you get the latex to show on wordpress without having it downloaded to a server?

  121. Pingback: LaTeX Holiday Fun! - Asymptotia

  122. Warren says:

    Here’s a test:

    [tex]
    \def\bigface#1{
    \setlength{\unitlength}{.5mm}
    \begin{figure}[t]
    \begin{picture}(0,0)(-320,-20)
    \put(0,0){\circle{24}}
    #1
    \end{picture}
    \vskip-.3in
    \end{figure}}
    \bigface{\put(-4,3){\circle{4}}
    \put(4,3){\circle{4}}
    \put(-3,3){\circle*{2}}
    \put(3,3){\circle*{2}}
    \put(0,-1){\oval(12,6)[b]}
    \put(0,-7){\line(0,1){3}}
    \put(0,-4){\oval(4,10)[b]}}
    [/tex]

  123. Warren says:

    another test:

    [tex]
    \setlength{\unitlength}{.5mm}
    \begin{figure}[t]
    \begin{picture}(0,0)(-320,-20)
    \put(0,0){\circle{24}}
    \put(-4,3){\circle{4}}
    \put(4,3){\circle{4}}
    \put(-3,3){\circle*{2}}
    \put(3,3){\circle*{2}}
    \put(0,-1){\oval(12,6)[b]}
    \put(0,-7){\line(0,1){3}}
    \put(0,-4){\oval(4,10)[b]}
    \end{picture}
    \vskip-.3in
    \end{figure}
    [/tex]

  124. Warren says:

    yet another test:

    [tex]
    \begin{picture}(0,0)(-320,-20)
    \put(0,0){\circle{24}}
    \put(-4,3){\circle{4}}
    \put(4,3){\circle{4}}
    \put(-3,3){\circle*{2}}
    \put(3,3){\circle*{2}}
    \put(0,-1){\oval(12,6)[b]}
    \put(0,-7){\line(0,1){3}}
    \put(0,-4){\oval(4,10)[b]}
    \end{picture}
    [/tex]

  125. Warren says:

    hope I don’t get banned for too much failed garbage:

    [tex]
    \begin{picture}(0,0)
    \put(0,0){\circle{24}}
    \put(-4,3){\circle{4}}
    \put(4,3){\circle{4}}
    \put(-3,3){\circle*{2}}
    \put(3,3){\circle*{2}}
    \put(0,-1){\oval(12,6)[b]}
    \put(0,-7){\line(0,1){3}}
    \put(0,-4){\oval(4,10)[b]}
    \end{picture}
    [/tex]

  126. Warren says:

    Nobody’s reading this thread anymore, right?

    [tex]
    \begin{picture}(30,30)
    \put(15,15){\circle{24}}
    \put(11,18){\circle{4}}
    \put(19,18){\circle{4}}
    \put(12,18){\circle*{2}}
    \put(18,18){\circle*{2}}
    \put(15,14){\oval(12,6)[b]}
    \put(15,8){\line(0,1){3}}
    \put(15,11){\oval(4,10)[b]}
    \end{picture}
    [/tex]

  127. Warren says:

    I guess mimetex isn’t really latex

    [tex]
    \begin{picture}(300,300)
    \put(150,150){\circle{240}}
    \put(110,180){\circle{40}}
    \put(190,180){\circle{40}}
    \put(120,180){\circle*{20}}
    \put(180,180){\circle*{20}}
    \put(150,140){\oval(120,60)[b]}
    \put(150,80){\line(0,10){30}}
    \put(150,110){\oval(40,100)[b]}
    \end{picture}
    [/tex]

  128. Warren says:

    zzzzzzzzz………..

    [tex]
    \begin{picture}(300,300)
    \put(150,150){\circle{240}}
    \put(110,180){\circle{40}}
    \put(190,180){\circle{40}}
    \put(120,180){\circle*{20}}
    \put(180,180){\circle*{20}}
    \put(150,140){\oval(120,60)}
    \put(150,80){\line(0,10){30}}
    \put(150,110){\oval(40,100)}
    \end{picture}
    [/tex]

  129. Warren says:

    [tex]\begin{picture}(300,300)\put(150,150){\circle{240}}\put(110,180){\circle{40}}\put(190,180){\circle{40}}\put(120,180){\circle*{20}}\put(180,180){\circle*{20}}\put(150,140){\oval(120,60)}\put(150,80){\line(0,10){30}}\put(150,110){\oval(40,100)}\end{picture}[/tex]

  130. Warren says:

    ignore me

    [tex]
    \begin{picture}(300,300)
    \put(150,150){\circle{240}}
    \end{picture}
    [/tex]

  131. Warren says:

    Maybe circles are the problem?

    [tex]
    \setlength{\unitlength}{.5mm}
    \begin{picture}(0,0)(-320,-20)
    \put(0,0){\oval(24,24)}
    \put(-4,3){\oval(4,4)}
    \put(4,3){\oval(4,4)}
    \put(-3,3){\oval*(2,2)}
    \put(3,3){\oval*(2,2)}
    \put(0,-1){\oval(12,6)}
    \put(0,-7){\line(0,1){3}}
    \put(0,-4){\oval(4,10)}
    \end{picture}
    [/tex]

  132. Warren says:

    maybe not

    [tex]
    \begin{picture}(0,0)(-320,-20)
    \put(0,0){\oval(24,24)}
    \put(-4,3){\oval(4,4)}
    \put(4,3){\oval(4,4)}
    \put(-3,3){\oval*(2,2)}
    \put(3,3){\oval*(2,2)}
    \put(0,-1){\oval(12,6)}
    \put(0,-7){\line(0,1){3}}
    \put(0,-4){\oval(4,10)}
    \end{picture}
    [/tex]

  133. Warren says:

    latex for pictures is obsolete anyway

    [tex]
    \begin{picture}(20,20)
    \put(0,0){\oval(24,24)}
    \put(-4,3){\oval(4,4)}
    \put(4,3){\oval(4,4)}
    \put(-3,3){\oval*(2,2)}
    \put(3,3){\oval*(2,2)}
    \put(0,-1){\oval(12,6)}
    \put(0,-7){\line(0,1){3}}
    \put(0,-4){\oval(4,10)}
    \end{picture}
    [/tex]

  134. Warren says:

    time to read the manual

    [tex]
    \begin{picture}(300,300)
    \put(150,150){\oval(240,240)}
    \put(110,180){\oval(40,40)}
    \put(190,180){\oval(40,40)}
    \put(120,180){\oval*(20,20)}
    \put(180,180){\oval*(20,20)}
    \put(150,140){\oval(120,60)}
    \put(150,80){\line(0,10){30}}
    \put(150,110){\oval(40,100)}
    \end{picture}
    [/tex]

  135. Peter Fred says:

    [tex]x^2[/tex]

  136. Peter Fred says:

    [tex]P_c=g_{s}\rho R[/tex]

    [tex]F_{nite}=g_s\rho R (\pi R^2)[/tex]

    [tex]F_{day}=(g_s-\Delta g)\rho R(\pi R^2)[/tex]

    [tex]F_{net}=\Delta g \rho\pi R^3[/tex]

    [tex]\Delta g \rho\pi R^3=({GM_\odot m_\oplus}/{R_{AU}^2})*(3/4)[/tex]

    [tex]({GM_\odot m_\oplus}/{R_{AU}^2})*(3/4)[/tex]

  137. Peter Fred says:

    [tex](\frac{GM_\odot m_\oplus}{r_{AU}^2})*(3/4)[/tex]

  138. Peter Fred says:

    [tex]\Delta g \rho\pi r^3={\frac{GM_\odot m_\oplus}{r_{AU}^2}*(3/4)[/tex]

  139. Peter Fred says:

    [tex]{\frac {V^2} {r_{AU}}}g \rho\pi r^3 \approx {\frac{GM_\odot \oplus}{r_{AU}^2}*(3/4)[/tex]

  140. Peter Fred says:

    [tex]{\[\frac {V^2} {r_{AU}}\]}\g \rho\pi r^3 \approx {\frac{GM_\odot \oplus}{r_{AU}^2})[/tex]

  141. Tester John says:

    test
    tex

    \bfseries{Hello}
    $\delta_{5} \times \alpha^{\sum i}$
    /tex

  142. Tester John says:

    [tex]

    \bfseries{Hello}
    $\delta_{5} \times \alpha^{\sum i}$
    [/tex]

  143. Tester John says:

    [tex]

    \bfseries{Hello}
    $ \delta_{5} \times \alpha^{\sum i}$
    [/tex]

  144. Guido says:

    [tex]e^{i \pi} + 1 = 0[/tex]

  145. Guido says:

    [tex]\sum_{k=0}^{\infty} \cfrac {k!} {(2k + 1)!!} = cfrac \pi 2[/tex]

    Cool

  146. Guido says:

    Messed up

    [tex]\sum_{k=0}^{\infty} {\cfrac {k!} {(2k + 1)!!}} = {\cfrac {\pi} {2}}[/tex]

  147. Pingback: think again! » Blog Archive » Math stuff in comments

  148. test says:

    [tex] \sum_{k=1}^{n} \frac{1}{n^3} [/tex]