To bring some beauty into our lives:

[CaliforniaPeggy]

&t=4s

It's just over 3 minutes long, and so beautiful! You won't be sorry.

[SheltieLover]

1. TY, Peggy!

[Permanut]

2. Thanks, Peggy, we need that.

[wordstroken]

3. Beautiful!! And calming.

Thank you so much, Peggy.
🙏

[CoopersDad]

4. 1/(φ) (φ)-1 or: 1/.6180339 1+.6180339

Phi defines the proportion that creates the golden section.
The Fibonacci Sequence is roughly an expression of that proportion.
I remember using a simple calculator to derive the value of Phi long before the Internet was there to help.



All I knew was that you could keep adding a square to the long side of a rectangle of that proportion and end up with a rectangle of the same proportion. Trial and error brought me to a value that I have memorized to this day: 0.6180339... (an irrational value).

The equation that I used based on the geometry: X+1 = 1/X

[Mousetoescamper]

5. Thanks, Peggy!

[CaliforniaPeggy]

6. You're very welcome, my dear Mousetoescamper!

[electric_blue68]

7. Sooo lovely! TY! ...

Last edited Tue Nov 12, 2024, 04:14 AM - Edit history (2)

I didn't get some of the algebra stuff, and the circle and angles ..but that ok.
Maybe if I watch it more I might. Pretty enough to watch repeats. 👍

I have drawn the fibonachi arc on graph paper up to the 55 squares, not sure I had enough squares, and room for the next number sequence at ?89.
It's fun!