crystal clear mathematics logo


Sign up to my Newsletter


Transformations and Symmetry

One of Scott Kim's Ambigrams showing the entire English alphabet written in symmetrical groups of lettersYou are now entering the officially wonderful and weird world of transformations and symmetry.  It transpires that symmetry is not only observed on the macro level (our bodies are basically symmetric to look at), but on the quantum level as well.  Symmetry plays a huge role in our understanding of how the universe functions.

One of Scott Kim's Ambigrams showing the word mathematics written in such a way that it looks the same upside downThe most basic forms of symmetry are reflective symmetry (or line symmetry) as shown in Scott Kim’s ambigram of the English alphabet at left, and rotational symmetry as shown in his design of the word mathematics at right (view it upside down).

I first encountered Scott Kim‘s work in OMNI magazine in the late 1970s.  I would love to show you many examples of what he does with symmetry and agree with him that this artistic skill should be included in mathematics lessons.  Please visit Scott Kim’s website and take time to read some of his blogs about mathematics and teaching (as well as seeing samples of his amazing artwork)!

Mathematicians are fascinated by symmetry and, ultimately, ask questions about symmetries that are not simply geometric.  There are symmetries in algebra and relationships in quite a few areas of mathematics.  They all have the idea of balance or of conserving something.

I hope you enjoy this journey with me.









By far the best educator I have been subject to in my schooling life. Apart from showing me with the utmost clarity the many concepts of mathematics, Graeme has inspired me to better myself in everything that I do in school and in my life. His dedication to his craft is truly admirable, and this level of dedication to helping the student achieve is something that is extremely hard to find. If you’d want anyone on your side during HSC mathematics, it’d be Graeme.
Harry B (student, 2012)

See all Testimonials

Sign up to my Newsletter

Copyright © Crystal Clear Mathematics | All Rights Reserved

Website Design: | Photography: