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 Cone of curves In mathematics, the cone of curves (sometimes the Kleiman-Mori cone) of an algebraic variety formula_1 is a combinatorial invariant of much importance to the birational geometry of formula_1. Let formula_1 be a proper variety. By definition, a (real) "1-cycle" on formula_1 is a formal linear combination formula_5 of irreducible, reduced and proper curves formula_6, with coefficients formula_7. "Numerical equivalence" of 1-cycles is defined by intersections: two 1-cycles formula_8 and formula_9 are numerically equivalent if formula_10 for every Cartier divisor formula_11 on formula_1. Denote the real vector space of 1-cycles modulo numerical equivalence by formula_13. We define the