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 drawing aid with many different smoothly-varying radiused curves on it; the manual drafter can fit the French curve to some known reference points and draw a smooth curved line between them. A spline is a flexible ruler, usually rubber or plastic coated with a metal "backbone", which can be smoothly shaped to follow a desired curve and allows drawing a smooth line between initial reference points. Sometimes a spline is temporarily held in position with small weights. A perspective machine is an instrument designed to create perspective drawings. Silk-paper -like translucent drafting paper that wrinkles when wetted. It is