I am about to embark on a series of posts concerning geometric constructions. I feel that it is important for every craftsperson to be able to translate their ideas into a layout drawing. Geometry is the tool that will best enable this function. In order to create a thing we must first be able to visualize the thing. Both in our mind’s eye and on paper.
For some, myself included, this comes easily. These people are most often referred to as visual learners or right brain thinkers. These people can construct items within their mind’s eye. Visualizing each part and how it is to fit with the next. They can turn it, change it’s size and even add color to it. They know what the item will look like long before the physical construction begins.
For others this visualization does not come easily. Its a skill that must be learned and practiced. These are the left brain thinkers. They think in words and in logical sequences. Computational mathematics come easily for these people and they prefer things to be absolute.
Educators once understood and embraced this fundamental difference in how people think and interact in the world around them. This pedagogical approach led to manual training programs being instituted to allow each type of thinker to grow in their real world skills. The system of Sloyd is an example of this. The idea being that each side of the brain must be nurtured in order to fully educate an individual. Each person must develop skill sets in both the abstract and the concrete world in order to be a ‘well-rounded’ productive member of society.
Mathematics has the unique ability to bridge the two types of thinking together. For the right brain, visually based, thinkers there is geometry. It can be easily visualized in the mind’s eye as well as physically manipulated in the real world. For the left brain, logic based, thinkers there is algebra, trigonometry and calculus.
Art, music, wood and metal shop, cooking and technical drawing programs help the right brain thinkers link practical applications to the theoretical lessons they are being taught. For the left brain thinkers the reverse applies. These type of programs help them to link from theoretical to practical applications.
OK, I waded a little deeper into that pool of thought than I had intended. My point is that in order to create something you must be able to first visualize that thing. Geometry can be used as the link between the two. For right brain, visual, people it links the brain to the paper. Geometry gives them the ability to bring what they visualize in their mind into the physical world. For the left brain, logical, thinkers it links the paper to the brain. Geometry gives these people the ability to link the physical world into logical and sequential terms that they can best identify with.
So long story long, that’s why all the geometry.