## Study Block 7

A tricky one this.

Have barely written much in quite a while. In fact, since I completed my first assignment – something I will post here once the course is over.

We’re going back to geometry with study block 7. For me, shape and geometry is fascinating. I haven’t particularly studied this aspect of maths in a long while, but my degree’s dissertation was based around the Fibonacci sequence, the golden ratio and its appearance in art and nature.

Absolutely wonderful stuff, with some complex maths.

My recent fascination, a clear one given the theme of this site, are fractals.

Given 4 shots of a fractal, can you order them from

least zoomedinto most zoomedit? The point is that this ishardto do. Fractals are objects which areequally complex and look similar on all scales– therefore it is inherently difficult to tell how zoomed in you are. If you looked over someone’s shoulder, and saw them looking at a shot of the Mandelbrot set, it is entirely possible that at their zoom-level the entire set would span the size of the observable universe!

The above quote and image are from Matt Henderson’s maths and science blog.

Again, the maths is complex, literally, and not something I totally understand (that knowledge has somewhat left my mind). However, I feel that something like this would be a good thing to explore in the primary school setting. Not only are they incredibly beautiful, they can provide a stimulus for ordering exercises, they provide a new and exciting set of shapes to explore, they can make great displays.

Let’s expand:

- Sierpinski Triangles can be made using equilateral triangles – which in turn can be created through paper folding.
- Investigating the Sierpinski Triangles can lead to such questions as: what fraction of the triangle is left after one step, two steps…? Is there a pattern?
- Linking Sierpinski’s Triangle to Pascal’s Triangle, see below. This involves investigating the pattern in Pascal’s Triangle and shading all even numbers.

###### Related articles

- Understanding Fractal and L-System (solid1610.wordpress.com)
- Breathtaking Mandelbrot Videos – Now in Brilliant 3D (techie-buzz.com)
- Fun with fractal squiggles (i-programmer.info)
- Fractal Menger sponge made from Post-Its (boingboing.net)