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To bring some beauty into our lives: (Original Post) CaliforniaPeggy Nov 11 OP
TY, Peggy! SheltieLover Nov 11 #1
Thanks, Peggy, we need that. Permanut Nov 11 #2
Beautiful!! And calming. wordstroken Nov 11 #3
1/(φ) (φ)-1 or: 1/.6180339 1+.6180339 CoopersDad Nov 11 #4
Thanks, Peggy! Mousetoescamper Nov 11 #5
You're very welcome, my dear Mousetoescamper! CaliforniaPeggy Nov 11 #6
Sooo lovely! TY! ... electric_blue68 Nov 12 #7

CoopersDad

(2,863 posts)
4. 1/(φ) (φ)-1 or: 1/.6180339 1+.6180339
Mon Nov 11, 2024, 11:13 AM
Nov 11

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

electric_blue68

(17,977 posts)
7. Sooo lovely! TY! ...
Tue Nov 12, 2024, 02:08 AM
Nov 12

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!

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