Denys Fisher Denys Fisher Denys Fisher (11 May 1918 – 17 September 2002) was an English engineer who invented the spirograph toy and created the company Denys Fisher Toys. He left Leeds University to join the family firm, Kingfisher (Lubrication) Ltd. In 1960 he left the firm to set up his own company, Denys Fisher Engineering, in Leeds. In 1961 the company won a contract with NATO to supply springs and precision components for its 20 mm cannon. Between 1962 and 1964 he developed various drawing machines from Meccano pieces, eventually producing a prototype Spirograph. Patented in 16 countries, it went on
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