Daily Science | Fibonacci Sequence: The Shining Pearl in the Crown of Mathematics

Fibonacci sequence - 1, 1, 2, 3, 5, 8, 13, 21... The first and second terms of the sequence are 1, and the following terms are the sum of the previous two adjacent terms. It was first known to people when the famous "rabbit breeding" problem was raised in the "Complete Abacus" by Italian mathematician Fibonacci. In fact, the charm of mathematics is not limited to paper. The Fibonacci sequence has always played a vital role in studying various phenomena in nature, human beings and social life, and even in practical applications in daily production and life.

A coincidence in nature

Wandering in the wild and stopping at the outskirts, we will find the Fibonacci sequence everywhere. It can be the small golden needles on the small balls of winter cacti, or the "Fibonacci Golden Angle" spirals on various carnivorous plants such as aloe vera, or the total number of branches and leaves that appear on the streets of winter cities. The flower disk and the arrangement of melon seeds in the sunflower also show a magical state of gradually spreading outward because they conform to the mathematical laws of the traditional Fibonacci sequence. These magical phenomena may be the perfect display of different forms of traditional mathematical aesthetics in the Fibonacci sequence. We have reason to marvel at the coincidence of these wonderful phenomena in nature with the Fibonacci sequence.

The inexhaustible source of brand design

Take the well-known Apple logo design as an example. In fact, Apple's logo is not just a simple apple with a bite taken out. The circular arcs and mathematical lines in it also contain mathematical rigor and logic. The logical deduction of the "golden spiral" is also based on the Fibonacci sequence arrangement. In addition, the logo of Brazil's Boticario also follows the structure of the "golden spiral". In "The Da Vinci Code", the "golden spiral" also appears as an important clue.

It can be seen that designing a brand based on the Fibonacci sequence and applying it to products can fully cater to the different aesthetic feelings of most people and give people a soft and friendly feeling, so that the design aesthetics of the entire brand and the company's purpose and concept can be perfectly presented.

A practical art

In the process of industrialization, there is the time-grating measurement technology that originated from the Fibonacci sequence. In the fields of management and operations research, there are flow analysis models based on the Fibonacci sequence. In the application field of modern information electronic technology, based on the Fibonacci sequence law, a novel construction method for semiconductor structured cyclic low-density parity check number coding is proposed. This method achieves convenience on various scale integrated circuits while still maintaining excellent error correction control performance.

In addition, in the financial field, the Fibonacci sequence is also shining. The future market can be deduced from important turning points, and this sequence applied to stocks is called the Fibonacci cycle. We can use the complete timetable of the time operation of the two different bands of rising and falling to accurately calculate the overall market operation volume and duration of all the two different bands of falling and rising in the future band market. It is worth mentioning that the Fibonacci sequence optimization method is the foundation of modern finance.

The Fibonacci sequence is not just watching over us from an ivory tower. On the contrary, it is not only integrated with nature, but also closely related to our production and life. When you stare at the Fibonacci sequence on paper, it is also staring at you around you.

(Author's unit: Mathematics Culture Team of Huazhong Agricultural University's Master Studio)