Spirograph a hypocycloid. 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.
Geometric calculus the correspondences of the differential form its derivative and its Hodge dual embed the theory of differential forms within geometric calculus. Following is a diagram summarizing the history of geometric calculus. Geometric calculus In mathematics, geometric calculus extends the geometric algebra to include differentiation and integration. The formalism is powerful and can be shown to encompass other mathematical theories including differential geometry and differential forms. With a geometric algebra given, let "a" and "b" be vectors and let "F(a)" be a multivector-valued function. The directional derivative of "F(a)" along "b" is defined as provided that the limit exists, where the