An astroid is a flat curve described by a point of a circle of radius rolling along the inner side of a circle of radius. In other words, an astroid is a hypocycloid with a module. The name of the curve in the form of “Astrois”.
The radius of the larger circle (a)
The radius of the smaller circle (b)
Chord length (l)
b = a / 4
l = 2 * a * sin( π/4 )
Р = 6 а
S = 3/8 π a2