“Geometry is the knowledge of the eternally existent” Plato
For the past few years I have been teaching a math class, Visual Geometry, at the College of Visual Arts in St. Paul, something that would come as a shock to any of my previous math teachers. I agreed to lead the class for a couple of reasons, one that a major part of the class was teaching orthographic drawing, something I had been doing for a number of years (and I was trained as an architect so I believed I could teach anything). The other part of the classand the most fundamentalwas a study of geometry and numbers in what is one way a very simple level, and in another asks the students to consider the concepts that form the very core of all mathematical, physical and cosmological thinking.
When I started teaching, ten years ago, my first class was an introductory architectural drawing class that covered both observational and scaled orthographic drawings. As an introductory class, the students were diverse in the skill and experience they had. Many had had drafting classes, but few were comfortable with observational drawing. Getting them to see and to draw what they see was the main thrust of the class. The Visual Geometry is very different; most of the students are very accomplished in observational drawing, and wary of math.
In the College of Visual Arts class, we approach geometry in much the way the ancient Greeks did, developing fairly complex figures constructed with only a pencil, compass and unmarked straight edge. We do proofs, but they are visual proofs. We draw square roots (starting with, of all things, a square). We explore the mathematical nature of the growth of plants, the shape of diatoms, chemistry, physics, art and the universe as a whole. I think this approach to mathematics increases the accessibility for nonscientists to understand the current thinking about roots of math and science.
It also hearkens back to the days when a learned person had a wide breadth of knowledge and was able to see the interconnectedness of art, math, music, and the movement of the planets. One of the final assignments for my class is an open ended creative project, where the student is to apply and explore these concepts in an artistic endeavor. I receive a wide variety of projects, from paintings and prints to music and clothing. The quality and depth of course range widely, but I usually see a spark of interest and understanding generated. Even more gratifying is when students bring these ideas into their studio projects, often with great success. I believe designers should be well versed in the fundamentals of how the universe works, and with the easy and accessible variety of writings and websites devoted to the subject, there is no excuse not to imitate the Greeks and put this sort of knowledge at the center of our creative thinking.
Below are links to sites and books that are written for the lay person and are a good entry to understanding what are both the early fundamentals of mathematics and the newest thoughts on math and science.
Gödel, Escher, Bach, by Douglas R. Hofstadter, published over thirty years ago, opened the door to the kind of writing that allows those uninitiated into the arcane mysteries of science to develop understanding of the major ideas at work in mathematics, including its role in music and art.
The Road to Reality, by Roger Penrose, who developed an aperiodic tiling system, delves deeper into mathematics and physics
Math Forum has a good list compiled by G. Brandenburg of MIT is available from the website.
Also, the popular media has been doing more reporting on the cutting edges of our understanding of the universe especially around such interesting and possibly terrifying subjects such as CERN’s Large Hadron Collider and Minnesota’s own Soudan Underground Laboratory. These sites do a good job of explaining the science behind what is being looked for in these large experiments designed to study the smallest particles.
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