Geometric Bites

Today I was watching a video about how to construct a dodecahedron . In the first part of the clip, it was shown how to get the golden ratio with a specific type of geometric construction . I was absolutely intrigued by it and decided to figure out if the construction did indeed yield the result phi. Remarkably and beautifully, I was able to confirm the result. My workings are shown below. I live for these eureka moments! Part 1 Part 2 Part 3   Part 4

Recently, I produced some recursive geometric art that got a pretty good amount of attention on the internet. Here it is: So, what was the secret of its success? It was a solid geometric drawing I made beforehand. With that solid geometric drawing, I was able to see the proportions required to produce my animation. There is a clarity that geometric drawings bring because of their rigidity . As you can see in the image above, the squares get smaller . Their lengths decrease by a factor of 1/2 with each iteration . When these lengths are applied to vertical and horizontal lines what you get is pure mathematical magic... The pattern in my video. How about the equations ? Well, if I tell you everything it would be like revealing the entire story of a great movie before you've watched it. I would hate to spoil your creative experience. :-)

This proof solves a popular internet geometry problem found here: https://twitter.com/RonySarker71/status/1428469920443076609 By utilising the radius of the circle , one can arrive at the conclusion that y= √(ax). If a=1, then you get y= √(x).