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
Differential geometry of curves space curves are only distinguished by the way in which they bend and twist. Quantitatively, this is measured by the differential-geometric invariants called the "curvature" and the "torsion" of a curve. The fundamental theorem of curves asserts that the knowledge of these invariants completely determines the curve. Let (i) formula_1, (ii) formula_2, and (iii) formula_3 be a non-empty interval of real numbers. Then a vector-valued function of class formula_5 (i.e., the component-functions of formula_6 are formula_7-times continuously differentiable) is called a parametric formula_5-curve or a formula_5-parametrization. Note that formula_10 is called the image of the parametric curve. It is important