The importance of Geometry and Geometric Thinking
This is geometric thinking for both the mathematician and the artist. Geometry for all. I believe it speaks creatively to young minds, or indeed adult minds.
It’s not about pushing a utilitarian use of maths, but an organic wholeness of thought. It is about the discovery of form and shape that connect to the nature of the child. In the first instance it is about a visual literacy of shape recognition at an early age.
Geometric Thinking is geometry and the development of thought.
What is a mathematics training?
Outside of its everyday utilitarian uses, maths and science are at the forefront of cultural development. That is to say that the latest advancements in medicine or space exploration come about because of our growing understanding of the sciences and higher maths. These advancements shape who we are as humans.
So how does geometric thinking affect our shaping of thoughts?
Steiner believed in the power of teaching the right thing at the right time to the child. He believed that the development of the cultural civilisation of mankind can be reflected in the development of the child. Steiner also put a high emphasis on the importance of art and practical activities in education.
“A new dimension in the study of form is opened up by a knowledge of projective geometry; it underlies the theory of metamorphosis in living forms and also in artistic creation” Olive Whicher
To grasp the concept of projective geometry is to leave behind the Euclidean geometry of measure and analysis that we all know and was embedded into us. It will help us to think of the qualities of mathematical forms and to build a way of thinking of these forms as moving and growing.
Example 1: the hexagonal net. Starting with 3 points on a horizon line we can draw a net of hexagons using just straight lines. A net pattern can be picked out from the resulting drawing. They are all hexagons yet not equal sided ones, yet the properties of the Hexagon are true to the pattern. they may all be different but there is an underlying similarity to all of them. This is the process of geometrical metamorphosis.
Example 2 : transformation of a triangle In this example of the triangle transforming into recognisable natural leaf shapes we follow an easy geometric construction repeated around the triangle to create the leaf form. The process of experiencing this happening is a strongly felt moment.
There is that question that a child always asks when driving in the car and looking out the window;
“Why is the moon/sun following us ?”
I’ve never worked out how to answer that question in a meaningful and mathematical way.
It is a projective geometrical question. It has baffled many artists and mathematicians of old. Form changes with movement and perspective and with the interplay of light. In its very essence, this is what projective geometry is.
Introducing a study of form which leaves behind the strict analysis of measurement can lead to experiencing shapes and form as a flow of dynamic changes. These forms can be recognised in nature.
Geometric forms in Nature
Yes… all these can be found in nature, just click the links to discover. And the experience of recognising and connecting with these forms in a true hands and heart type of way can be a very special experience. It moves you. And provides rich pastures for a curious mind to delve into. It is this thought process which is to be encouraged, which has the potential to bring about change.
And that is what I want to get into.