Astroid with two Constructions

The astroid is defined by these equations:
  c(t) = RR * [ cube(cos(t)), cube(sin(t)) ]
Of course it is a special case of the Hypocycloids with frequency = -3 and stick = 1. It is shown separately because of its second construction:
The tangent segment between the coordinate axes has constant length; it is often viewed as a ladder from the ground to a wall. The normals of the astroid are tangents of twice as large an astroid, rotated by 45 degrees. This pair of orthogonal ladders allows a simple circle & ruler construction of the astroid - watch the demo.