## Exploring the mathematical world through art

To know mathematics fully takes effort and struggle: the kind of struggle and effort that artists crave. In order to excel in either art or mathematics you need a tremendous amount of imagination, creativity and a zest to delve into the world of abstraction.

Some of the most interesting mathematical views of the world come in the form of art, and in particular, art that shows the natural world using shape and space.

Great examples are the Indigenous art of the Pacific Northwest of North America or the skin decorations of the Maori people of New Zealand. When you look closely at the visual art, you are struck by the mathematical principles that are applied. Very quickly you see the extensive use of geometric transformations, all of it derived from the world around us.

What is fascinating to me is how appealing things that follow mathematical constructs are to us. Art explores symmetry, translations, rotations and even quite advanced concepts like, let’s say, conformal transformation.

Walk around, look at the small and look at the large. Can you find symmetry? Can you find examples of reflections and other types of translations present in nature?

Inspired by traditional art techniques, can your learners explore and represent the real world using symmetry and geometric transformations? Can they create a representation of what they saw using shapes: i.e. can they draw a mountain range made solely out of varying triangles of different colours, or city buildings using only quadrilaterals? Is it possible to do it all using only regular polygons? Can they draw or transform what they see into new shapes, on new planes? Perhaps prompt learners to explore how they can draw a spider web being pushed by a strong wind.