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).
Technical drawing tool a device used for copying objects in an adjustable ratio of sizes. French curves are made of wood, plastic or celluloid. Some set squares also have these curves cut in the middle. French curves are used for drawing curves which cannot be drawn with compasses. A faint freehand curve is first drawn through the known points; the longest possible curve that coincides exactly with the freehand curve is then found out from the French curves. Finally, a neat continuous curve is drawn with the aid of the French curves. Rulers used in technical drawing are usually made of polystyrene.It is