Links Blogged: The Fibonacci Sequence, Spirals and The Golden Mean and More

The Golden Ratio: How to derive it a+b/a=a/b=1.618..

How to Calculate the Golden Ratio - https://www.masterclass.com/articles/golden-ratio-explained#a-brief-history-of-the-golden-ratio

 https://en.wikipedia.org/wiki/Golden_spiral: In geometry, a golden spiral is a logarithmic spiral whose growth factor is φ, the golden ratio.

Graphically: https://upload.wikimedia.org/wikipedia/commons/thumb/e/e9/GoldenSpiralLogarithmic_color_in.gif/440px-GoldenSpiralLogarithmic_color_in.gif

 

https://upload.wikimedia.org/wikipedia/commons/thumb/e/e9/GoldenSpiralLogarithmic_color_in.gif/440px-GoldenSpiralLogarithmic_color_in.gif

Fn = Fn-1 + Fn-2 where n>3 or n=3 http://jwilson.coe.uga.edu/EMT669/Student.Folders/Morris.Stephanie/EMT.669/Essay.3/Fibonacci.Essay.html

Special feature of the Golden Number is it has a similar conjugate: Golden Ratio Conjugate: 0.618..

1 / 0.618 = 1.618.. = 1 + 0.618


 

x2-x-1=0, x(x-1)=1, we get x=0 or x=1 unit circle

1.618 is one of the roots of x2-x-1=0



The Fibonacci Spiral


 

 

 

  • Spirals and the Golden Ratio

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Fibonacci numbers and Phi are related to spiral growth in nature.

If you sum the squares of any series of Fibonacci numbers, they - https://www.goldennumber.net/spirals/

 

 

 
 

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