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 Templates are also available for other geometric shapes such as squares and for drawing ellipses, as well as many specialized varieties for other purposes. There are also specific templates to provide user with the most common symbols in use in different branches of designing. For example, the architect templates can be used to draw different sized doors with their "opening arcs", building and equipment symbols and furniture. The templates also provide the symbols for thermal insulation. Two methods of drawing smooth curves in manual drafting are the use of French curves and flat splines (flexible curves). A French curve is