Constructing $\pi^2$ and e with straightedge and compass

f[x_, a_] = a - x^2;
Manipulate[
 Plot[{f[x, a], x},
  {x, -5, 5},
  PlotRange -> {{-5, 5}, {-5, 5}},
  Epilog -> {Red, PointSize[0.02], Point[{x, f[x, a]} /. # & /@ Solve[f[x, a] == x, x]]}
  ],
 {a, 1, 20, Appearance -> "Labeled"}]