Description: Exciting facts about the most beautiful number in the universe.
The Golden Ratio
What is Phi ( φ )
- If a/b is equal to (a+b)/a, then a and b are said to have the Golden Ratio.
- It is represented by Phi ( φ )
- The Golden Ratio is often called the most beautiful number in the universe.
Value of Phi (φ)
- PHI (φ) is an irrational, non-terminating number.
- φ = 1.61803398874....
Why extraordinary ?
- It can be visualized almost everywhere, starting from geometry to the human body itself.
- The Renaissance Artists called this "The Divine Proportion"
The Human Body
- If you divide the length from your head to toe by the that from your belly to toe, the ratio tends to φ.
- Length from top of head to shoulder divided by that from top of head to chin also gives φ.
- Length of your face divided by width of the face gives φ.
- Lips to eyebrow divided by length of the nose, approximates to φ.
- If you divide the length from your head to toe by the that from your belly to toe, the ratio tends to φ.
Plants
- A sunflower grows in opposing spirals, the ratio of its rotation's diameter the the next is 1.618... i.e. φ again !
- The ratio between the margin of a leaf to its veins (some plants) also gives φ.
DNA of Organisms
- The major groove and the minor groove of the DNA spiral is in the ratio of φ.
The Solar System
- The average of the mean orbital distances of each successive planet in relation to the one before, tends to φ.
- The rings of Saturn exhibit the golden ratio.
- Venus and Earth are linked in an unusual relationship involving φ.
Art and Architecture
- Some masterpieces based on the Golden Ratio.
Unique Property of φ
- The reciprocal of φ is 0.618 which is 1 less than itself.
- Therefore, you can flip the ratio and use 1.618 and 0.618 interchangeably !
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