Personal Discovery of the Golden Ratio
Construction of the Pentagon
Bored and lonely one evening, I recalled seeing someone demonstrate the construction of a pentagon. I have always liked pentagons and as a child I would draw them with a protractor and straight edge. I once tried to figure the ratio of the height to the width and also the bottom edge, so I could draw them without the protractor. I was so intrigued by the fact that someone figured this out, that I set about to at least understand the triangle that was generated in the construction. As I was using my TI55, I kept getting numbers that were magically related to each other. I would typically just run numbers and calculations back and forth, constantly seeing connections. This was never taught to me in school.
Being a recent Richard Buckminster Fuller enthusiast, I had bought a copy of Synergetics, which I told myself I would one day read. Knowing that there were all kinds of irrational numbers in Fuller’s book, I cracked it open and ended up finding on page 480 of Synergetics Vol I, the same angles and I found this to be extremely gratifying.
The following day I went to the library to find out about these numbers and found them in a book called, “Geometry and Liberal Arts”. I had run into the Golden Ratio, something that I had never heard about and it really inspired me.
I searched through Fuller’s Synergetics and not once is the golden ratio mentioned. This puzzles me to this day. Thinking that knowledge of the golden ratio would make Synergetics more interesting and accessible, I decided that my little part in Fuller’s Design Science Revolution would be to show how the golden ratio is prevalent in all five-fold symmetric forms including Geodesic Domes.
