DescriptionSmoothed Octagon.svg	English: The construction of a smoothed octagon.
Date	20 March 2009
Source	Own work by uploader, made in Mathematica, and heavy processing in Inkscape.
Author	Inductiveload
Permission (Reusing this file)	Public domainPublic domainfalsefalse I, the copyright holder of this work, release this work into the public domain. This applies worldwide. In some countries this may not be legally possible; if so: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

l = Sqrt[2] - 1;
m = Sqrt[6*Sqrt[2] - 8]*(Sqrt[2] + 1)/2;

hyper = ParametricPlot[
   {m/l * Cosh[t], 
    m * Sinh[t]},
   {t, -Pi, Pi}];

adj = Plot[
   {(Sqrt[2] + 1)*(x - 2),
    -(Sqrt[2] + 1)*(x - 2)},
   {x, 2, 10}];

asymp = Plot[
   {l*x, -l*x},
   {x, 0, 10}];

Show[
 {hyper,
  adj,
  asymp},
 AspectRatio -> Automatic,
 PlotRange -> {{0, 4}, {-2, 2}}
 ]