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).
Affine geometry of curves arclength). Then, In concrete terms, the matrix "C" is the pullback of the Maurer–Cartan form of the special linear group along the frame given by the first "n" derivatives of x. Affine geometry of curves In the mathematical field of differential geometry, the affine geometry of curves is the study of curves in an affine space, and specifically the properties of such curves which are invariant under the special affine group formula_1 In the classical Euclidean geometry of curves, the fundamental tool is the Frenet–Serret frame. In affine geometry, the Frenet–Serret frame is no longer well-defined, but it is possible