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.

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.

"Rolling" means that the point of the rolling circle that touches the
"street"-circle has velocity zero.

A motion with a point at rest is a rotation around this rest point. Applied to the drawing pen on the stick

this means: the curve tangent at the point just drawn is orthogonal to its connection to its rest point.

Compare Cycloid

A motion with a point at rest is a rotation around this rest point. Applied to the drawing pen on the stick

this means: the curve tangent at the point just drawn is orthogonal to its connection to its rest point.

Compare Cycloid