Crystal Math XVII: Opinion of φ

[⛄]

[muon2]

I voted freedom number because it is the golden ratio, but it only links geometry and algebra. I couldn't go beyond that since it's not part of my favorite equation which binds the symbols of counting (1), geometry (π), arithmetic (0), algebra (i), and calculus (e).

e^iπ + 1 = 0

[Associate Justice PiT]

     Rather pretentious for invoking a greek letter to describe a simple sum of a rational and an irrational number.

[H.E. VOLODYMYR ZELENKSYY]

It's quite beautiful.

[Boston Bread]

Another neat fact:

φ = sqrt(1+φ)

We can replace the φ on the right-hand side with the given definition of φ:

φ = sqrt(1+sqrt(1+φ))

Repeat infinitely and you get:

φ = sqrt(1+sqrt(1+sqrt(1+sqrt(1+...)))) with infinite square roots

[⛄]

Rather pretentious for invoking a greek letter to describe a simple sum of a rational and an irrational number.

Is this rhombic triacontahedron "pretentious" or beautiful?
Doesn't deserve it its own greek letter?

[Associate Justice PiT]

     Nothing wrong with being a little pretentious. I just have found (1+sqrt(5))/2 very useful to work with, and I usually remember the golden ratio by that. I am quite impressed by the rhombic triacontahedron, I will admit. To think, a solid composed of rhombi.

     As an aside, when I was in high school, we went over sequences. We had to do a few different operations with a few different sequences, most of which were simple. One thing we had to do was find the 100th term of the Fibonacci sequence. I did not know that the golden ratio could be used to calculate the nth term of the Fibonacci sequence, so I spent hours calculating it through recursion. Years later, I discovered the truth about it.

[muon2]

I prefer the rhombic dodecahedron. It is one of the few solids that can tessellate space and appears naturally in crystals such as garnet and in the bonding structure of diamond. You did say this is Crystal Math.