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).
Denys Ovenden Denys Ovenden Denys Ovenden was born on April 1, 1922. His preoccupation with drawing began very early, since there are drawings on the fly-leaves of books from that period. His natural history interest began. Watercolor is the basic medium for his work, with occasional "gouache" for highlighting or detail. His preferred working surface is a "fashion" type board, "CS2 not surface" being the favorite. Reference sources are most important, and Denys uses a body-live, pinned or pickled, to work from, as pinned and set specimens can be misleading due to shrinkage, discoloration or loss of parts. He does use photographs