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).
Cone of curves extremal rays of the cone cannot accumulate. If in addition the variety formula_1 is defined over a field of characteristic 0, we have the following assertion, sometimes referred to as the Contraction Theorem: 3. Let formula_48 be an extremal face of the cone of curves on which formula_33 is negative. Then there is a unique morphism formula_50 to a projective variety "Z", such that formula_51 and an irreducible curve formula_8 in formula_1 is mapped to a point by formula_54 if and only if formula_55. (See also: contraction morphism). Cone of curves In mathematics, the cone of curves (sometimes the Kleiman-Mori