Wednesday, 1 February 2012

Paper Protractors

Inspired by this video from Vi Hart on 'Angle - a trons', year 10 students today set about making some of their own paper protractors! It is a fascinating exercise and a brilliant way to look at geometrical reasoning and proof. No measuring is done here, just reasoning. For example, starting with a square piece of paper and by folding, how many different angles can you make? How can you prove they are what you say they are? What do you have to assume as true to start with? It is surprising what can be achieved by combining a simple set of logical steps. For example, folding an angle in half or in to thirds will create that fraction of the angle. Once you know some angles you can figure out the others using a series of 'If Then' statements. A running theme through the exercise was the notion of considering how we go from axioms to theorems and how each theorem is dependent on the original axioms used to build it! Lovely, practical, engaging, and fun!

This video helped us get started,

And this link from the exploratorium was useful too!

Some pictures to follow!


  1. Fantastic! There's a kind of delightful simplicity in this. And it's satisfyingly a thing to make, handle - "kinaesthetic". And, as you say, there's such a clear sequence of reasoning that's almost jumping out of the paper!

  2. This is cool! I like how your class does a lot of hands-on activities in class. I like hands on activities because it really helps me understand the material! That is so cool!

  3. Wow! I think I want to make myself one of these paper protractors! Thanks!

  4. Wow that was helpful