Fibonacci Sequence (Marcos Pinilla) by Marcos Pinilla Fernández-Roldán

INTRODUCTION

marcospinilla — 2024-12-04 10:24:56 UTC

The Fibonacci sequence is one of the famous mathematical sequences. It starts with 0 and 1, and each subsequent number is the sum of the two preceding ones: 0,1,1,2,3,5,8,13,21,34...

HISTORICAL CONTEXT

marcospinilla — 2024-12-04 10:25:24 UTC

The sequence was introduced by Fionacci in his book Liber Abaci in 1202. Fibonacci used this sequence to model the growth of a population of rabbits under ideal conditions.

This succession has numerous applications in science. It also appears in biological configurations, such as in the arrangement of leaves on the stem.

MATHEMATICAL DEFINITION

marcospinilla — 2024-12-09 15:43:16 UTC

The Fibonacci sequence can be defined recursively as:

F(n)=F(n-1)+ F(n-2), with F(0)=0 and F(1)=1

APPLICATIONS

marcospinilla — 2024-12-09 15:43:38 UTC

This succession has numerous applications.

-Nature: Fibonacci numbers appear in the distribution of leaves on a stem, the relationship between the veins of tree leaves, the relationship between the thickness of the main branches and the trunk, the distance between the spirals of a pineapple.

-Architecture and Art: The sequence is closely related to the Golden Ratio, which has been used to create aesthetically pleasing desings.The Fibonacci sequence allows us to create works with proportions that resemble those of nature, and which are therefore more beautiful and harmonious. Thanks to the Fibonacci sequence, architects have managed to achieve a balance and visual harmony that has been widely recognized in the history of architecture.

-Technology: It is applied in to optimize data transmission, computer science and data structures like the Fibonacci heap.

VISUALS

marcospinilla — 2024-12-09 15:43:46 UTC

Spiral Representation: The Fibonacci sequence is often visualized as a spiral, with the size of each square corresponding to a Fibanacci number.

Nature Examples:

-Sunflower seed arrangement.

-Pine cones and pineapples.

-Artichoke flowers.

-In the proportions of the human

body.

INTERESTING FACTS

marcospinilla — 2024-12-09 15:44:04 UTC

Fibonacci numbers appear in Pascal's Triangle as the sum of the diagonal entries.
The ratio between consecutive Fibonacci numbers approximates the Golden Ratio.
Starting from 0 and 1, they are added in pairs, so that each number is equal to the sum of its previous two.

REFLECTION

marcospinilla — 2024-12-09 15:44:19 UTC

While researching the Fibonacci sequence, I have found it very interesting how this sequence is so present in our daily lives.