What did the little acorn say when he grew up? Geometry (Gee, I’m a tree)!

Sorry for the ‘teacher’ joke.

As soon as we begin to enquire about *shapes,* we are ‘speaking’ geometry. Originally, it was the mathematics of measuring the Earth, surveying blocks of land for farming, for example. In Egypt, geometry was used to replace boundary markers between properties after the Nile flooded each year. The term geometry comes from the Greek words γη (ge-) or γαια (Gaia) meaning earth, ground or land, and μέτρον (métron) meaning measure.

Geometry can be regarded as the discipline of studying abstract shapes with their properties and relationships. It can also be thought of in very practical terms. Tradespeople use geometry every day of their lives, making sure walls or frames are square, having the correct gradients for trusses, roofs, pathways, stormwater, etc. I have workmen on my roof at the moment, replacing corrugated iron sheeting. The art of cutting the sheeting to fit involves some clever geometry!

All the different facets of geometry result from our asking curious questions. At least, *someone* asked these questions:

- how do these shapes compare? ~ Congruency and Similarity
- how can I alter (or not alter) these shapes? ~ Transformations and Symmetry
- how do shapes fit together? ~ Tessellations
- how can I calculate distances/lengths diagonally across objects? ~ Pythagoras’ Theorem
- how can I measure lengths and angles inside circles and what properties do circles have? ~ Circle Geometry
- how can different places be connected? ~ Graph Theory
- what does ‘being connected’ mean, and what fundamental properties of shapes are preserved when a shape is distorted? ~ Topology

I had the privilege of being one of Graeme’s students in 2005. As a creatively minded individual I struggled greatly with Mathematics and was falling behind in my HSC studies. Under his careful and creative tutelage I began to truly understand Mathematics for the first time in my life. Graeme patiently taught me to master mathematical concepts in ways I could understand. In the week intensive I spent with him he taught me the entire HSC course, and I went on to receive a Band 6. I cannot recommend him highly enough.

Roxanne G (student, 2005)

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