The catenary is the theoretical shape a hanging chain or cable will assume
    when supported at its ends and acted on only by its own weight.

    y = a * cosh(x / a)
      = a * (exp(x / a) + exp(-x / a)) / 2

    a = {0.5, 1, 2}

    y = {0.5 * cosh(x / 0.5), 1 * cosh(x / 1), 2 * cosh(x / 2)}

    from Wikimedia Commons
    plotted with cubic bezier-curves
    the bezier-controll-points are calculated to give a very accurate result.
    acuracy is 0.000001

    symbols in "Computer Modern" (TeX) font embedded
    created with a plain text editor using GNU/Linux

    about: http://commons.wikimedia.org/wiki/Image:Catenary-pm.svg
    source: http://commons.wikimedia.org/
    rights: GNU Free Documentation license,