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).
Geometric function theory Geometric function theory Geometric function theory is the study of geometric properties of analytic functions. A fundamental result in the theory is the Riemann mapping theorem. The following are some of the most important topics in geometric function theory: A conformal map is a function which preserves angles locally. In the most common case the function has a domain and range in the complex plane. More formally, a map, is called conformal (or angle-preserving) at a point formula_3 if it preserves oriented angles between curves through formula_3 with respect to their orientation (i.e., not just the magnitude of the angle).