This toy represents the relation between p(pi) and the radius of a circle, as well as its relation to revolutions, waves, sines and cosines. The relation is no longer thought as 2pr, instead 2r (the diameter of the circle) is related to p as three whole parts of the circumference of a circle, and one open ended infinite part. This ratio can be shown most effectively with the help of a string of 2r length.
Beyond visually teaching the meaning of p, this symbol should also become the modern peace symbol of a new rational generation.
This toy can be used to teach Apollonius notion of duality, using the simple construction of a hollow tube, three moving pieces, and three cafeteria straws. The motion of any part affects the other parts maintaining the duality relation, as can be seen on the close-up in the next illustration.
This toy shows the axis line of the Fibonacci squares and spiral.
This third toy is a more advance game using electric and magnetic fields to define symmetries within the notes at every quadrant. The final position should show all notes associated by some kind of symmetry, for example, mirror, inversion, rotation, translation, or multiple transforms.
Quadratic ratios of Spirals