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).
The Sleep of Reason Produces Monsters The Sleep of Reason Produces Monsters __notoc__ The Sleep of Reason Produces Monsters () is an etching by the Spanish painter and printmaker Francisco Goya. Created between 1797 and 1799, it is the 43rd of 80 etchings making up the suite of satires "Los Caprichos". Goya imagines himself asleep amidst his drawing tools, his reason dulled by slumber and bedeviled by creatures that prowl in the dark. The work includes owls that may be symbols of folly and bats symbolizing ignorance. The artist's nightmare reflected his view of Spanish society, which he portrayed in the "Caprichos" as demented, corrupt, and