Spirograph Spirograph Spirograph is a geometric drawing toy that produces mathematical roulette curves of the variety technically known as hypotrochoids and epitrochoids. It was developed by British engineer Denys Fisher and first sold in 1965. The name has been a registered trademark of Hasbro Inc. since 1998 following purchase of the company that had acquired the Denys Fisher company. The Spirograph brand was relaunched worldwide with original product configurations in 2013 by Kahootz Toys. In 1827 English architect and engineer Peter Hubert Desvignes developed his "Speiragraph", a machine to create elaborate spiral drawings, intended to prevent bank note forgeries. The mathematician
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