Nature, The Golden Ratio, and Fibonacci, too …

Plants can grow new cells in spirals, such as the pattern of seeds like in beautiful sunflower.

The spiral happens naturally because each new cell is formed after a turn.

“New cell, then turn, then another cell, then turn, …” as in a pineal gland, that’s why in the vatican plasa, a decoration of pinga was put in place, but was named pigna instead.

So, if you were a plant, how much of a turn would you have in between new cells?

If you don’t turn at all, you would have a straight line and that is a very poor design.

You would want something round that will hold together with no gaps, so why not try to find the best value for yourself? try different values, like …

0.75, or 0.9, or maybe 3.1416, 0.62, etc …

Remember, you are trying to make a pattern with no gaps from start to end, and it doesn’t matter about the whole number part, like 1. or 5. because the full revolutions points you back in the same direction.

If you got something that ends like 0.618 (or 0.382 which is 1-0.618) then, congratulations, you are a successful member of the plant kingdom!

That is because the Golden Ratio (1.61803…) is the best solution to this problem, and the sunflower has found this solution in its own natural way.

Because if you choose any number that is a simple fraction (example: 0.75 is 3/4, and 0.95 is 19/20, etc), then you will eventually get a pattern of lines stacking up, and hence lots of gaps.

But the Golden Ratio (its symbol is the Greek letter Phi) is an expert at not being any fraction.

It is an Irrational Number, meaning you cannot write it as a simple fraction, but more than that … it is as far as you can get from being near any fraction.

Just being irrational is not enough. Pi or 3.141592654 … is also irrational, and unfortunately it has a decimal very close to 1/7 or 0.142857… so it ends up with 7 arms.

Also, there is a special relationship between the Golden Ratio and Fibonacci Numbers

0, 1, 1, 2, 3, 5, 8, 13, 21, … each number is the sum of the two numbers before it.

If you take any two successive (one after the other) Fibonacci Numbers, their ratio is very close to the Golden Ratio.

So, just like you naturally get seven arms if you use 0.142857 (1/7), you tend to get Fibonacci Numbers when you use the Golden Ratio.

This interesting behavior is not just found in sunflower seeds. Leaves, branches and petals can grow in spirals, too.

Why? So that new leaves don’t block the sun from older leaves, or so that the maximum amount of rain or dew gets directed down to the roots.

In fact, if a plant has spirals, the rotation tends to be a fraction made with two successive Fibonacci Numbers, for example:

And that is why Fibonacci Numbers are very common in plants. 1,2,3,5,8,13,21 … occuring in an amazing number of places.

The equivalent of 0.61803 rotations is 222.4922 degrees, or about 222.5°, about 137.5° that is called the “Golden Angle”.

So, next time you are walking in the garden, look for the Golden Angle, and count petals and leaves to find Fibonacci Numbers, and discover how clever the plants are … like the pinga in vatican!

Reblogged this on parasapinga.