NATURE'S KEY TO BEAUTY

Why the flowers have 3 or 5 petals? Why we do not have circular or square mobile screens? Why the galaxies are spiral?

1. GOLDEN NUMBERS

1 1 2 3 5 8 13 21 34 ....
The above sequence is called Fibonacci sequence. Here, any number is the sum of preceding two numbers. The nature follows this series everywhere. Many flowers have 3 or 5 petals. Mostly 3 leaves are arranged spirally in a stem. Also pineapple scales follow 21 and 34 pattern.

2. GOLDEN RATIO:

In the above series, divide 3 by 2, you get 1.5. As the series progresses, dividing any number by the preceding number, you get the stable ratio 1.61803.... an irrational constant.
If you divide length by the breadth of mobile screen or length and breadth of credit card, mostly you will get this ratio. This ratio appeals to our eyes.
Bone lengths from tip of the finger to the elbow and facial features follow this ratio.

3. GOLDEN ANGLE:
Divide the total angle of the circle 360 degree by the golden ratio 1.618..., we get 222.5 degree. Subtract this 222.5 from 360, we get 137.5 degree - that is golden angle.
Go to a plant. Look at leaves on a stem. Mark one leaf. the immediate next leaf is present at angle 137.5 degree from the marked one and also at a slight height from the marked leaf. The next second leaf has also grown at an angle 137.5 degree from the preceding leaf. It goes on repeating. The advantage: all leaves will get adequate sunlight. The top layer of the leaves will not shadow the bottom layers. This happens only for the golden angle. All other angle simply fails.

4. GOLDEN SPIRAL:

Let us represent Fibonacci sequence in geometrical form.
1,1,2,3,5,8 ...
1. Construct one unit length squares side by side.
2. Add a another square of size 2 units above it.
3. Put a square of length 3 units left side.
4. Add a square of size 5 units at the bottom.
5. Repeat the process, move clockwise as far as the paper permits.
6. Join the diagonally opposite corners; starting from square one; again move clockwise; till you reach the last square.
7. You get a golden spiral which is geometrical representation of golden series.
The galaxies, arrangements of leaves, pattern of sea-shells, pattern of seeds in a sun-flower follow golden spiral.
These golden entities are yet another way to understand the nature.

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