Another way to get the golden ratio, using geometry and algebra
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