Hypocycloid prove that an epicycloid with "k" cusps moves snugly inside one with "k"+1 cusps. The evolute of a hypocycloid is an enlarged version of the hypocycloid itself, while the involute of a hypocycloid is a reduced copy of itself. The pedal of a hypocycloid with pole at the center of the hypocycloid is a rose curve. The isoptic of a hypocycloid is a hypocycloid. Curves similar to hypocyloids can be drawn with the Spirograph toy. Specifically, the Spirograph can draw hypotrochoids and epitrochoids. The Pittsburgh Steelers' logo, which is based on the Steelmark, includes three astroids (hypocycloids of four cusps).
Plastic number Plastic number In mathematics, the plastic number (also known as the plastic constant, the minimal Pisot number, the platin number, Siegel's number or, in French, le nombre radiant) is a mathematical constant which is the unique real solution of the cubic equation It has the exact value Its decimal expansion begins with . The powers of the plastic number satisfy the third-order linear recurrence relation for . Hence it is the limiting ratio of successive terms of any (non-zero) integer sequence satisfying this recurrence such as the Cordonnier numbers (better known as the Padovan sequence) the Perrin numbers and the