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Kaleidoscope Films

In a Mathematics Teaching article (MT206), Geoff Faux contributed the special issue on Visualisation with his article: ‘Kaleidoscope’

I started my visualisation session at Brampton by showing a still from Kate Mackrell's Kaleidoscope. “What do you see?” was my question.

“I was immediately struck by one student's description of a symmetry and reflection line that was quite at odds with what I was holding in my head. Possibly because I had seen the whole thing moving on a number of occasions, I was hanging on to the mirrors I knew about and not the bisectors of the angles between two mirrors! So I learned that there are other ways of seeing. We worked on how many mirrors there were. I think the idea of ‘mirror’ must have happened because I used the word ‘kaleidoscope’ when I put the picture up on the screen.

“I animated the figure and we watched it change and develop. I stopped it and asked if the students would like to construct their own kaleidoscopes. There was enthusiasm, so I went ahead. We established that there were three rotating mirrors and that there were a number of shapes, each of which were reflected in each of the mirrors.

“Using Cabri, I demonstrated and they copied on their own computers, setting up the mirrors. I set up a point and drew a circle with that point as centre. I placed a point on the circle and showed them how to move that point round the circle, both with the mouse and by animating it.”

Read the full article here