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Mathematical notation has been chosen, or developed over time, because it is highly efficient at communicating a huge amount of information in a short amount of space. It is almost as if the natural tendency of mathematical notation is to act a as a space-saving algorithm; the information content to notation ratio in mathematics is extremely high.

Most attempts to communicate this notation to computers has been difficult at best, with MathML being much too complex for humans to actually write, and LaTeX often requiring much looking up of the various short cuts that been developed, particularly for beginners.

Here's an example of some LaTeX to produce a mathematical diagram.

\png \definecolor{blueblack}{RGB}{0,0,135} \color{blueblack} \begin{picture}(4,1.75) \thicklines \put(2,0.01){\arc{3}{3.53588}{5.8888}} \put(.375,.575){\line(1,0){3.25}} \put(1.22,1.375){\makebox(0,0){\footnotesize$ds$}} \put(.6,.5){\makebox(0,0){\footnotesize$x=0$}} \put(3.36,.5){\makebox(0,0){\footnotesize$x=\ell$}} \dottedline{.05}(1.0,.575)(1.0,1.10) \put(1.0,.5){\makebox(0,0){\footnotesize$x$}} \dottedline{.05}(1.5,.575)(1.5,1.40) \put(1.5,.5){\makebox(0,0){\footnotesize$x+dx$}} \put(1.22,.65){\makebox(0,0){\footnotesize$dx$}} \dottedline{.04}(0.6,1.12)(1.25,1.12) \put(1.0,1.14){\vector(-1,-1){.45}} \put(.58,0.83){\makebox(0,0){\footnotesize$T$}} \put(.77,1.05){\makebox(0,0){\scriptsize$\theta(x)$}} \put(1.18,1.16){\makebox(0,0){\scriptsize$\theta(x)$}} \dottedline{.04}(1.5,1.41)(2.1,1.41) \put(1.5,1.44){\vector(4,1){.67}} \put(2.22,1.59){\makebox(0,0){\footnotesize$T$}} \put(1.95,1.45){\makebox(0,0){\scriptsize$\theta(x+dx)$}} \end{picture}

Can you tell what the final output of this LaTeX will be? (See http://www.forkosh.com/mathtex.html for the answer)

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