Spirograph Bruno Abakanowicz invented the Spirograph between 1881 and 1900. It was used for calculating an area delimited by curves. Drawing toys based on gears have been around since at least 1908, when "The Marvelous Wondergraph" was advertised in the Sears catalog. An article describing how to make a Wondergraph drawing machine appeared in the "Boys Mechanic" publication in 1913. The Spirograph itself was developed by the British engineer Denys Fisher, who exhibited at the 1965 Nuremberg International Toy Fair. It was subsequently produced by his company. US distribution rights were acquired by Kenner, Inc., which introduced it to the United
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