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 metallic means first described by Vera W. de Spinadel in 1998. Donald E. Knuth has suggested referring to formula_5 as "High Phi", along with suggesting a special typographic mark for it. 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