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𝜑 generator

2015-04-09, post № 15

mathematics, programming, Python, #Fibonacci, #generates, #generator, #golden ratio, #𝜑, #phi, #ratio, #simulation, #terminal, #the golden ratio

This program generates 𝜑, also called the golden ratio. It creates the fibonacci sequence \big\{1,1,2,3,5,8,13,\dots\big\} and divides the newly generated number by the last one. In theory this program would generate exactly [1] 𝜑.

phi-generator.png

Fibonacci sequence

  • \text{Start: }x_1=1\text{ and }x_2=1
  • \text{Generation: }x_n=x_{n-1}+x_{n-2}
  • 1+1=2
  • 1+2=3
  • 2+3=5
  • 3+5=8
  • 5+8=13
  • 8+13=\dots

The golden ratio (𝜑)

  • \phi\text{ is the ratio between }x_n\text{ and }x_{n-1}\text{.}
  • \phi=\frac{x_n}{x_{n-1}}
Source code: phi-generator.py

Footnotes

  1. [2020-07-08] Assuming infinite time and memory it would compute 𝜑 in its limit.