Īmy Shell-Gellasch (Montgomery College), "Mathematical Treasure: Hypotrochoid Kinematic Model by M. The full set of the Smithsonian Schilling kinematic models can be found at. With the advent of computer aided design software, mathematical models are now museum pieces or curios in display cabinets in university mathematics or engineering departments. The green point on the radius of the disc traces a green curve inside the ring, and the red point on the extension of the radius of the disc traces a curve that extends past the radius of the ring.īy the early years of the 20th century, these types of models were losing popularity with educators. The blue point on the circumference of the disc traces a blue five-pointed star shape referred to as a hypocycloid. In this model, three hypotrochoids are generated. It includes Graph Cartesian functions, relations, and inequalities, plus polar, parametric, and ordinary. Hypotrochoids are members of the family of curves called trochoids-curves that are generated by tracing the motion of a point on the radius of a circle as it rolls along another curve-and include the well-known cycloids. Graphmatica is an equation plotter with numerical and calculus features. This model produces hypotrochoids, curves formed by tracing a point on the radius or extension of the radius of a circle rolling around the inside of another stationary circle. Hypotrochoids (ca 1900), kinematic model by Martin Schilling, series 24, model 3, number 331, Smithsonian Institution negative number DOR2013-50214. They fall roughly into two categories: linkages and models that produce trochoids. The Smithsonian houses ten of these models, most from the University of Michigan. One of the largest publishers of mathematical models, both static and kinematic, was the firm of Martin Schilling of Leipzig, Germany. Models that depict geometric curves produced by constrained motion were called kinematic models. During the latter half of the 19th century and into the 20th, educators and engineers used models to visualize mathematical curves and surfaces.
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