ANIMAL FIBONACCI SEQUENCE IN NATURE HOW TO
ANIMAL FIBONACCI SEQUENCE IN NATURE SERIES

ANIMAL FIBONACCI SEQUENCE IN NATURE HOW TO

This is the next concept we see on the animation: how to configure the structure formed by the sunflower seeds. These two circular segments are accomplishing too with the same golden proportionality, but on this case the value of the angle formed by the smallest of them is another irrational number, we can simplify and round it as 137.5 ºĪnd this value is deeply present in nature. That is, the angular proportional relationship between two circular segments: We are going one step further on the animation by introducing a new concept, maybe less known but equally important, the Golden Angle. The higher the value, the greater the approximation (consider that Phi, like any irrational number, has infinite decimals). You have an example at right (we will see another one): if we divide each value in the Fibonacci Series by the previous, the result tends to Phi. JUST A CURIOSITY: it isn't evident on the animation, but there is a deep connection between the Fibonacci Sequence and Golden Ratio. And we find in many works created by the mankind in art and architecture, from the Babylonian and Assyrian civilizations to our days, passing through ancient Greece or the Renaissance. The result of this ratio (ie the division of a by b) is an irrational number known as Phi -not to be confused with Pi- and an approximate value of 1.61803399…įormerly was not conceived as a true 'unit' but as a simple relationship of proportionality between two segments. It fulfills this ratio, also known as the Golden Ratio or Divine Proportion: the ratio of the sum of the quantities ( a+b) to the larger quantity ( a) is equal to the ratio of the larger quantity ( a) to the smaller one ( b).

This is very special rectangle known since ancient times.

ANIMAL FIBONACCI SEQUENCE IN NATURE SERIES

See the complete process on the following series of illustrations: We start from a simple square to get that and use a classic method that requires only a ruler and drawing compass. It introduces the concept of Golden Ratio by constructing a Golden Rectangle. Once it has appeared the Nautilus we advance to the second part of the animation. Or you could explain in a more 'genteel' way, saying that I have taken an artistic license -) Therefore I must confess that I did a kind of cheat with this animation. The truth is that this is something I discovered when I had completely finished the screenplay for this project and I was too lazy to change. It's funny because if you perform this search at Google Images: “ spiral + nautilus” you will see how many images suggest that this shell is really based on the construction system described above.īut this isn't correct, as it's outlined on this other page. IMPORTANT NOTE: while watching the animation conveys the idea that the Fibonacci spiral (or the Golden Spiral, it doesn't matter) is on the origin of the shape of a Nautilus, this isn't absolutely right. It's something similar to what happens when we try to approach to an ellipse by drawing an oval using circular segments: the result is not the same as a true ellipse. I have introduced a small optical correction in the animation in order to get the resulting curve more like a true Golden Spiral(more harmonious and balanced), as explained on this plate. Then we draw a quarter circle arc (90°) within each little square and we can easily see how it builds step by step the Fibonacci Spiral, looking at right graphic. And they are arranged in the way how we see in the diagram at left. We will create first a few squares that correspond to each value on the sequence: 1x1 - 1x1 - 2x2 - 3x3 - 5x5 - 8x8, etc. This is the next thing to be shown on the animation, appearing just after the first values on the succession: the process of building one of these spirals. The values of this sequence have been appearing in numerous applications, but one of the most recognized is the Fibonacci Spiral, which has always been used as an approximation to the Golden Spiral (a type of logarithmic spiral) because it is easier to represent with help of a simple drawing compass. This is an infinite sequence of natural numbers where the first value is 0, the next is 1 and, from there, each amount is obtained by adding the previous two. So it is known as Fibonacci Sequence, even although it had been described much earlier by Indian mathematicians. This is a very famous and recognized sequence since many centuries ago in the Western World thanks to Leonardo of Pisa, a thirteenth century Italian mathematician, also called Fibonacci. The animation begins by presenting a series of numbers.

Animal fibonacci sequence in nature