Have you noticed that many plants grow in spiral? The pineapple, for example, can have 8 scale spirals headed into one direction and 5 or 13 headed towards the other direction. If you look at the seeds of the sunflower, you will see at least 55, respectively 89, spirals crossing each other.

The cauliflower also displays spirals. Why do plants grow this way? Does the number of the spirals have any significance?

You should know first that plant organs, like stem, leaves and flowers, grow from a central growth point called meristem. Every new structure, named primordium, develops from this center, growing to a new direction and forming a certain angle with the previous primordium. In most plants, the primordia grow at a certain angle one towards another, so that their disposition is in spiral.

What value does this angle have? Imagine you have to project a plant around a development point so that the primordia are located compactly, without wasting space. Let's say that each primordium grows at an angle equal to two fifths of a cycle. The problem is that each fifth new structure would grow exactly on the same place and direction.

This way, they would form rows that waste space. In fact, any finite fraction of a cycle would dispose the primordia in rows, wasting space. Only a "golden angle" of 137o 30' would form a compact disposition for the primordia.

Why is this angle unique? It's ideal because it cannot be expressed by a finite decimal fraction of a cycle. 5/8 tends to the golden angle, 8/13 even more and 13/21 much more but none can express precisely the golden number which is about 1.618.

That's why when a new primordium develops following the golden angle, there will never be two primordia growing in the same direction. Instead of forming radiuses from the central stem, the primordia form spirals. Computer simulations of the primordia's development from a central point achieve visible spirals only when the angle between the new primordia approaches more the golden angle.

The effect is lost even with just one tenth of a degree deviation from the golden angle. The number of spirals resulted by the development of the plants following the golden angle is a number from "the line of Fibonacci".

Humans and the golden number

Greek mathematicians, presumably the disciples of Pythagoras, discovered the golden number during the 6th century BC. In their search for harmonic geometrical figures, the ancient Greeks found a perfectly balanced regulated (with equal sides) pentagon, inside which they could make a five-armed star called pentacle. When they made the ratios between different parts of the pentacles, the number 1.618 was found by tens of times.

Then, they discovered the same proportions in the human body. Divide the total height of your body with the part going from the navel to your feet or divide the length of the part under the navel with that over the navel: the result will be very close to the golden number. Make the same with the phalanges of your fingers. See the ratio between the first and the second, the second and the third. The drawing of a human with stretched feet and hands makes a pentacle.

The Greek mathematicians saw in the golden number the harmony of the Universe and a "divine proportion".

The numbers following the golden rule make a line, first mentioned by the Italian mathematician Leonardo Fibonacci during the 13th century. In this progression, each number is the sum of its previous two numbers: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 and so on.

The term of 'golden number' was introduced during the 17th century. Artists, painters and architects used the golden number as a basic rule in their works.

The Egyptian pyramids followed the golden number: divide the height of a side of Khufu pyramid with half of its base and you will get the golden number. During the 5th century BC, Phidias used the golden number when constructed the Parthenon of Athens. The length and the height of the front, but also the dimensions from the inner temple follow the golden number. Many medieval Gothic cathedrals and churches follow the rule of the golden number. The cathedral of Chartres (France) makes a cross following the proportions of the golden number.

But paintings are those that abuse of it. Leonardo da Vinci has many works dedicated to the "golden section". Each of these paintings is a web of geometrical figures obeying the golden number. Picasso too used the number. Moreover, the ratio between the handle of a violin and its cage, too, is a golden number.

Nature and the golden number

Many flowers with a spiral disposition have a number of petals from the Fibonacci line: many flowers have 5 petals, bloodroot 8, ragwort 13, chickweed 21, chrysanthemum 34, 55 or 89. Leaf growth on many trees follows the Fibonacci line. Not only pineapples, but also pine cones follow the Fibonacci line.

Even fruits and vegetables follow the Fibonacci line. A banana has 5 flanks. Cut an apple transversally: its seed disposition describes a pentacle.

Animals too follow the golden number. The shell of a Nautilus or a snail makes a spiral respecting the golden angle. A starfish forms a perfect pentacle.