Notes on Prime Numbers
  • Introduction
  • Revision History
  • What Do You Mean Large
  • Enter bc
  • Pi with bc
  • C++
  • Ramanujan's constant
  • The Largest Known Prime
  • The Golden Ratio
  • Random Numbers
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The Golden Ratio

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Last updated 5 years ago

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References:

  • at the WikiPedia.

Two quantities are in their golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities:

(a + b)   a    (1 + sqrt(5))
------- = - =  -------------
   a      b         2

The Golden Ratio a.k.a. Phi is about 1.618. Phi is derived from the Fibonacci sequence:

1, 1, 2, 3, 5, 8, 13, 21, 34 ...

Each number in it is the sum of the preceding two numbers:

1+1=2, 2+1=3, 2+3=5, 3+5=8, 5+8=13, 8+13=21, 13+21=34 ...

The quotients of successive adjacent terms:

2  3  5  8      34
-, -, -, -, ... --
1  2  3  5      21

converge on Phi as you get further out.

Golden Ratio