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 for any formula_39. Given the image of a parametric curve, one can define several different parametrizations of the parametric curve. Differential geometry aims to describe the properties of parametric curves that are invariant under certain re-parametrizations. We thus have to define a suitable equivalence relation on the set of all parametric curves. The differential-geometric properties of a parametric curve (e.g., its length, its Frenet frame and its generalized curvature) are invariant under re-parametrization and therefore properties of the equivalence class itself. The equivalence classes are called formula_5-curves and are central objects studied in the differential geometry of curves. Two parametric