Fibonacci sequence in art and nature series#

Proportions can be found in architecture or in arts, as in poetry or music. The nautilus shell isn't actually related to the golden ratio. They may seem like the golden spiral, but they are just an approximation of the ancient ratio. Those spirals are actually the ones that are more mistaken and seen as made with the golden ratio. The easiest way to cover a surface is by using hexagons, as in the eyes of dragonflies, while growing a resistant shell to cover your body needs less energy if it’s spiral shaped! Since irregular shapes can often provide a better chance to survive (if your leaves are positioned irregularly, they will get more sun, how convenient it is!), nature found the laziest way to overcome the problem! This can happen in different ways: some of the shapes are regular, some of them are irregular. There’s a small truth to this statement, but it’s actually wrong! We can find the Fibonacci numbers in a lot of nature patterns, like in the stripes of a zebra or in the flowering of an artichoke, but that is just an evolutionary ploy.

You may have heard that the golden means can be found everywhere in nature, usually supported by the Fibonacci sequence. The Fibonacci number and the Golden Section in nature… Sometimes the evidence is clear and obvious, sometimes it is an assumption. Over time, we started to recognize the ratio and the numerical sequence everywhere, from geometry statements to mathematical relations, from arts to architecture, from biology to music. Although we don’t know when the golden ratio was first used, we know for certain that we use its geometrical representation since at least 300 BC, when Euclid first mentioned it.

The Fibonacci sequence was described around 1202 by the Italian mathematician Leonardo of Pisa, better known as Fibonacci, but it’s been already known in India and it’s been used in poetry and math. The ratio that can fulfill this statement is the infinite number above. In other words: two quantities are in golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities.

Fibonacci sequence in art and nature series#

Something that intrigued both artists and scientist is that if you divide a number of the series by the previous one in the line, the bigger the better, you have a number close to the golden ratio, that is the irrational number 𝜑 = 1/2 (1+5)= 1,6180339. At the end, you’ll end up with this sequence: 1 1 2 3 5 8 13 21… 55… 1597, and so on. This means that if you add 1 + 1 = 2, then 2 + 1 = 3, 3 + 2 = 5 and so on. These numbers form a sequence where the next number of the progression is the sum of the two previous, starting from 1 and 1. There is a mathematical sequence that has inspired humanity for centuries and which has been a hallmark to define beauty: the Fibonacci numbers. We already know that the ancient Egyptian architecture was constructed with extreme precision and we know that physicians have proven reality through numbers. Art often is related to the Fibonacci numbersįor thousands of years we have tried to solve the world we see and to reproduce it using mathematical formulas, or to shape it with the help of math.