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 family Denys family The surname Denys was borne by at least three prominent mediaeval families seated in Gloucestershire, Somerset and Devon in south-west England between 1166 and 1641. It is not known if any relationship existed between these families. The surname "Denys" is just one of many variant spellings of the name: "Denise", "Le Deneis", "Le Danies", "le Deneys" and most recently "Dennis", are some of the others. The family of Denys was apparently of Danish origin, and was recorded in early Norman charters in French as "le Deneys", meaning "The Dane", which was frequently Latinised by scribes as Dacus, being