Mathematical Toy Part 1

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

2014-07-30 14.56.36

Trammel_of_Archimedes_Small_White

 

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.

 

ellipse

 

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.

https://www.desmos.com/calculator/sz3roeuszm

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”

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One response to “Mathematical Toy Part 1

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

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