Mathematical Toy Part 1

A few months ago, I found a toy my grandfather had made.

2014-07-30 14.56.36



The toy was very simple and fun to play with. One thing stuck out to me. The handle seemed to make a circular motion, but the handle stuck out more on one side than the other did. If the handle was tracing a perfectly circular path, then the handle should always stay the same distance away from the block of wood. However, this was clearly not the case.

I took a pencil and (with the help of my uncle) carefully traced out the curve swept by the handle. The picture looked like this.




I instantly recognized the shape, an ellipse!

An ellipse is like a squashed circle. It is still symmetrical and smooth, but one side is longer than the other is. It astonished me that my grandpa could create a toy that would sweep out a perfect ellipse, with only two moving parts.

Below is an animation I created to model the toy.

In the next post, I will prove that the shape doesn’t just resemble an ellipse, but it IS an ellipse.

Endnote: after investigating this interesting toy myself, I discovered its actual name, “the Trammel of Archimedes”


1 Comment

Filed under Uncategorized

One response to “Mathematical Toy Part 1

  1. Pingback: Mathematical Toy Part 2 | the Math behind the Magic

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s