GRAPHMATICA EQUATION FOR HYPOTROCHOIDS FULL
GRAPHMATICA EQUATION FOR HYPOTROCHOIDS PLUS

Īmy Shell-Gellasch (Montgomery College), 'Mathematical Treasure: Hypotrochoid Kinematic Model by M.

GRAPHMATICA EQUATION FOR HYPOTROCHOIDS FULL

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.

GRAPHMATICA EQUATION FOR HYPOTROCHOIDS PLUS

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. Graphmatica draws mathematical graphs like, y x2 - 6x + 5 A powerful, easy-to-use, equation plotter with numerical and calculus features: Graph Cartesian functions, relations, and inequalities, plus polar, parametric, and ordinary differential equations. The blue point on the circumference of the disc traces a blue five-pointed star shape referred to as a hypocycloid.

In this model, the curves each have five nodes. The ratio of the radius of the rolling disc to the radius of the outer ring will determine the number of nodes the hypotochoid will have. In this model, three hypotrochoids are generated. I have been trying to use a computer to plot some hypotrochoids, but Ive run into some issues. An infinite number of hypotrochoids can be formed, depending on the distance of the tracing point from the center of the rolling circle. 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. 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.

Graphmatica equation for hypotrochoids