Golden Ratio (phi) Collection

Chip Rollinson, Jan 7, 2017

Table of Contents

  1. Geometry of the Golden Ratio
    1. Golden Rectangle/Ratio Defined
    2. Golden Rectangle - Iterated
    3. Golden Rectangle - Infinite Zoom
    4. Spirale de Fibonacci déployée
    5. Golden Rectangle - Construction
    6. Regular Pentagon Ratios
    7. The Fibonacci elephant
    8. Golden Triangle & Spiral
    9. Golden Triangles and Infinite Series
    10. Ellipse and Annulus - When are the areas the same?
  2. Math of the Golden Ratio
    1. Fibonacci Ratios
    2. Interesting Math of Phi (Part I)
    3. Interesting Math of Phi (Part 2)
    4. Videos - The Math of the Golden Ratio
  3. Golden Ratio Examples?
    1. Golden Ratio Examples? - Art & Architecture
    2. Golden Ratio Examples? - Nature
    3. Golden Ratio - Flowers
    4. Golden Ratio Examples? - Logos
    5. Videos - Golden Ratio in Nature and Art

1.

Geometry of the Golden Ratio

  • 1. Golden Rectangle/Ratio Defined
  • 2. Golden Rectangle - Iterated
  • 3. Golden Rectangle - Infinite Zoom
  • 4. Spirale de Fibonacci déployée
  • 5. Golden Rectangle - Construction
  • 6. Regular Pentagon Ratios
  • 7. The Fibonacci elephant
  • 8. Golden Triangle & Spiral
  • 9. Golden Triangles and Infinite Series
  • 10. Ellipse and Annulus - When are the areas the same?

1.1.

Golden Rectangle/Ratio Defined

– Chip Rollinson

1.2.

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1.4.

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1.5.

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1.6.

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1.7.

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1.8.

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1.9.

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1.10.

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2.

Math of the Golden Ratio

  • 1. Fibonacci Ratios
  • 2. Interesting Math of Phi (Part I)
  • 3. Interesting Math of Phi (Part 2)
  • 4. Videos - The Math of the Golden Ratio

2.1.

Fibonacci Ratios

The Fibonacci Sequence starts with the numbers 1,1... each successive number is found by adding the two numbers the precede it.[br][br]What happens to the ratio of one Fibonacci number to the number just before it as the numbers increase in the sequence? (Why?)
How about if you start with numbers other than 1 and 1? [br][br]Pick ANY two starting numbers enter them in the a_1 and a_2 boxes below:
– Chip Rollinson

2.2.

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3.

Golden Ratio Examples?

  • 1. Golden Ratio Examples? - Art & Architecture
  • 2. Golden Ratio Examples? - Nature
  • 3. Golden Ratio - Flowers
  • 4. Golden Ratio Examples? - Logos
  • 5. Videos - Golden Ratio in Nature and Art

3.1.

Golden Ratio Examples? - Art & Architecture

[size=100][size=150]Here are some examples of the Golden Ratio. Some people think that it's the most beautiful proportion. That's why it's called the "Golden Ratio" or the "Divine Proportion". Some people think it's a hoax. You can judge for yourself. [/size][/size]
[size=200]Many people believe that the Golden Ratio helps create the most beautiful compositions...[/size]
[size=150][size=200]Maybe not...[/size][/size]
– Chip Rollinson

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