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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.









Our daughter Angelina was home schooled and from the start did not like maths. Over the years I have battled through, trying 5 different programs along the way. Angelina was surviving but not enjoying the journey but, when it came to algebra, the future looked dim. A friend recommended Graeme to me as her three sons had been tutored by him. She could not recommend him more highly. My daughter has just finished year 12 maths and did very well, thanks to Graeme (that would be an understatement). Graeme has a love for his subject and a genuine interest in his students. Graeme seems to meets his students where they are and tailors the lessons to meet their individual needs and interests. Graeme not only explains concepts clearly, but we all found him an interesting, knowledgeable and humble man. We are extremely happy that Graeme was recommended to us. Now our daughter is looking forward to uni with a grateful heart. We also could not recommend Graeme more highly.
Angela K (parent, 2013)

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