When was the spirograph introduced

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Nipkow disk.. Because point obeys the usual law of circular motion, its coordinates in the new relative coordinate system obey:. In order to obtain the trajectory of in the absolute old system of coordinates, add these two motions:.

Now, use the relation between and as derived above to obtain equations describing the trajectory of point in terms of a single parameter :. It is convenient to represent the equation above in terms of the radius of and dimensionless parameters describing the structure of the Spirograph.

Namely, let. The parameter represents how far the point is located from the center of. At the same time, represents how big the inner circle is with respect to the outer one. Parameter is a scaling parameter and does not affect the structure of the Spirograph. Different values of would yield similar Spirograph drawings. It is interesting to note that the two extreme cases and result in degenerate trajectories of the Spirograph. In the first extreme case when we have a simple circle of radius , corresponding to the case where has been shrunk into a point.

Division by in the formula is not a problem since both and are bounded functions. The other extreme case corresponds to the inner circle 's radius matching the radius of the outer circle , i. In this case the trajectory is a single point. Intuitively, is too large to roll inside the same-sized without slipping.

If then the point is on the circumference of. In this case the trajectories are called hypocycloids and the equations above reduce to those for a hypocycloid. Culture Wikia Explore. Wiki Content. Duke Ellington DJ Shadow!!! Explore Wikis Community Central. Register Don't have an account? History Talk 0. Editions MSH. Retrieved 17 July Likewise, do they still make Spirograph? The well known toy version was developed by British engineer Denys Fisher and first sold in The Spirograph brand was relaunched worldwide with original product configurations in by Kahootz Toys.

The Spirograph is a mathematical toy, which you can use for drawing nice figures. In the simplest case it exists of a fixed circle, used as a template, and a smaller rolling circle with holes.

Roll it inside the bigger fixed circle. This Spirograph set is exceptional and it is among the best choices on the market. Cyclex Kit Spirograph. Spirograph Tin Set. Deluxe Games and Puzzle Spirograph Set. Stretch Armstrong is made of latex rubber filled with gelled corn syrup, which allows it to retain shape for a short time before shrinking to its original shape.