Okay, so I ran out of green paper but you have to admit that this Sierpinski tetrahedral structure made out of 256 individual tetrahedrons is pretty impressive. Each edge of the structure is 64cm long so I have had to be careful carrying it around school – it just about fits through the doors!
Two of my students also constructed a beautiful topper for our Christmas tree. Again it was done properly using a pair of compasses and consists of equilateral triangles. There are three of the snowflakes taped together to create a sort of pyramid that sits on top of tetrahedral structure.
The topper is another example of a fractal and is called a Von Koch Snowflake. You start with an equilateral triangle and draw three more equilaterals, which have sides a third of the original, in the centre of the three sides. Now do the same on the twelve new sides and repeat as many times as you like as shown in the diagram below.
Our Van Koch Snowflake began with an equilateral triangle of sides 9cm. The next iteration used 3cm equilaterals and we stopped once we’d done the 1cm triangles as this was fiddly enough using a pair of compasses.
Mathematics really is beautiful.