Our project is meant to do more research about spirographs and draw spirographs using Mathematica. We want to know the history of the spirograph. The Spirograph is a geometric drawing toy that produces mathematical curves known as hypotrochoids and epitrochoids. In 1638, French scientist René Descartes discovered the spiral. Then Jakob Bernoulli named it spira mirabilis (“miracle spiral”) for its mathematical properties in 1692. An instrument called a spirograph was invented by the mathematician Bruno Abdank-Abakanowicz between 1881 and 1900 for drawing spirals. The British engineer Denys Fisher developed the well-known version of the toy “Spirograph” and it was first sold in 1965.
Hypotrochoids and epitrochoids are two general types of spirograph. Hypotrochoids represent the spirographs that have the small circle roll inside the big circle. On the contrary, Epitrochoids are the spirographs that have the small circle roll outside the big circle. We manipulated the big circle radius, the small circle radius, and the distance from a point to the center in the hypotrochoid and Epitrochoid equations. This showed us that we can produce many types of hypotrochoids and epitrochoids such as the curate epiroulette and the hypocycloid. We also found many examples in real life of these spirographs.
