Sunday, August 16, 2020

Summary -

Be careful of information that comes to you without any form of analysis. Rather than take things as truth, do some research for yourself. Test out theories. Check multiple sources. See if those sources are respected and reliable.

Although what I describe below sounds and looks horribly mathematical (many artists hate math), that is not the takeaway. The takeaway is, critical thinking is in short supply around the globe. Don't let it be true of you.

The Story -

Although misinformation as always been around, the rise of the internet has made it more difficult to detect. It is hard to tell what is correct or incorrect when everything looks professional and published. Before the internet, it was not as easy to spread bogus information far and wide. But now it is way too easy.

What does this have to do with Art 5, 3-Dimensional Design?

People naturally will look to others for quick answers to problems, and when we do a google search, we find lots of resources. It is so easy to think, "Okay, that's what I saw on the internet, so it must be true."

I have a method I learned years ago on how to draw any regular polygon with a given side length. Rather than make a video on the subject, I decided to find one already made on YouTube (Since that time, I HAVE made my own video). Avoiding making my video brought me to a fascinating one of a different method of drawing a regular square, pentagon, hexagon, heptagon, octagon and nonagon- all based on the same side length. I watched through the whole video, then tried it at home. Wow, what a great method! I will show my class!

But then I wondered why they did not include the triangle in this approach. When I tested with the triangle, I realized it didn't work. So I carefully analyzed the entire concept and found that it was flawed. Not so much so that the average person could tell.

I was not satisfied with discovering it was wrong. I wanted to find out why. This lead me to doing a very accurate series of polygons via my old fashioned method, and they do not match what is shown in the new method.

I am no math whiz, so I had to look things up like, "the difference between arithmetic and geometric sequences". And then I did a search of numeric ratios, which lead me to some very esoteric scientific papers on silicon enrichment, parametrically forced patterns and quasipatterns, and then one about solar geometry, "a case for the Divine design of the solar system", which is an entire page of misinformation in itself.

The Source of Misinformation-

Below is the flawed video I found.

My Analysis-

This is a very interesting technique. I was wondering why a triangle was not included, so I did a test and the triangle does not work. It would not come out equilateral. That got me thinking. Is this system accurate? It turns out it is only good for the square and the hexagon, because those were the two polygons that the system was derived from. None of the others are accurate along the top one or two legs (one for even polygons, two for odd). Also, except for the square and hexagon, none of the angles are accurate. I tested this out by drawing the diagram in CAD so the dimensions and radius points would be accurate to 6 decimal points. After creating a series of regular polygons, from a triangle to a heptagon, and measuring the distances between their inscribed circle centers, I found that it is not an arithmetic sequence. Instead it is geometric.