When I was a kid I spent countless hours (and many pieces of cardboard) inventing new designs on my Spirograph with its wheels, circles, pins and colored pens. Little did I know the history and the science behind this wonderful toy.

Mathematician Bruno Abakanowicz invented the spirograph between 1891 and 1900 as a means of calculating an area delimited by curves. It wasn't developed into a toy until 1965 when British engineer Denys Fisher introduced the first Spirograph at the Nuremberg International Toy Fair. U.S. distribution rights where acquired by Kenner Inc and released in the 1966. The toy is now a registered trademark of Hasbro Inc since it bought the Denys Fisher company.

As you may (or may not) recall, the Spirograph consisted of two different sized rings with gear teeth inside and out, along with several different sizes of gear wheels. It also came with a piece of cardboard, as well as push pins to fasten the rings to the cardboard. I would then pick out a wheel, interlock the gear teeth, take out one of five or six colored pens, put the pen tip in one of several holes in the wheel and create a pattern. To continue I would grab a different colored pen and different hole in the wheel and repeat thus creating my masterpiece.

After doing the research for this article I realized that the Spirograph toy I so enjoyed as a child was developed through a series of mathematical formulas dealing with an axis and intersecting lines such as...

 

\begin{array}{rcl}<br /><br /><br /><br /><br /><br /><br /><br /><br /> x_c&=&(R-r)\cos t,\\<br /><br /><br /><br /><br /><br /><br /><br /><br /> y_c&=&(R-r)\sin t.<br /><br /><br /><br /><br /><br /><br /><br /><br /> \end{array}

or

\begin{array}{rcl}<br /><br /><br /><br /><br /><br /><br /><br /><br /> x(t)&=&R\left[(1-k)\cos t+lk\cos \frac{1-k}{k}t\right],\\[4pt]<br /><br /><br /><br /><br /><br /><br /><br /><br /> y(t)&=&R\left[(1-k)\sin t-lk\sin \frac{1-k}{k}t\right].\\<br /><br /><br /><br /><br /><br /><br /><br /><br /> \end{array}

The Spirograph has survived for almost fifty years and even today it can be purchased in digital format (kind of defeats the purpose for me) And to think, I thought I was just having fun!!