# Fractals and Their Applications

Thursday 14th November 2019

Linked to enrichment sessions for Year 9/10 students that we have recently delivered in County Durham & Sunderland on fractals and their applications, why not look closely at this fractal slice – a relative perhaps to Serpinski’s. What everyday bit of maths does this represent?

Note the resolution of this image may not allow you to see that each of the smallest triangles present is itself split into smaller triangles…and so on ad infinitum.

Hint: You may wish to consider the coloured triangles...

The answer may be surprising. It is actually a geometrical representation of the Decimal Place Value System.

Each triangle is decomposed into 10 smaller triangles and so on ad infinitum. Each coloured band represents a place value holder...We'll leave it up to the reader to investigate how this representation adhere's to the concept and how the representation itself can raise questions about number.

One may also ponder how any triangle number can be used to represent a Place Value System For instance one can use Serpinksi's Triangle to model a Tertiary Place Value System but since any $$n$$th place value system itself is just representative of a counting structure (and it is possible to convert any place value counting structure into any other) then this suggests the possibility of a geometrical transformation that will to transform one geometrical model into another. One may also consider the relevance of 10 being both a triangular number and a tetrahedral number and how the DPVS can be represented in 3D...

If you are interested in booking an enrichment session, or if you would like free in-house departmental PD (currently focussing on KS3/4 Ratio please get in touch: [email protected].

By Jeremy Dawson