Part 1: Secrets of the Fibonacci Sequence - Introduction and History

Introduction

The Fibonacci sequence is one of the most fascinating mathematical phenomena that has applications in many areas of life. From mathematics to nature, art and marketing, its influence is invaluable. In the first part of this series, we will look at what the Fibonacci sequence is, its history and its basic mathematical properties.

What is the Fibonacci sequence?

The Fibonacci sequence is a sequence of numbers in which each successive number is the sum of the previous two. It starts with the numbers 0 and 1 and the subsequent elements are 1, 2, 3, 5, 8, 13, 21 and so on.

Mathematically this can be written as: F(n)=F(n-1)+F(n-2)F(n) = F(n-1) + F(n-2)F(n)=F(n-1)+F(n-2)where F(0)=0F(0) = 0F(0)=0 and F(1)=1F(1) = 1F(1)=1.

History of the Fibonacci sequence

The sequence was introduced into mathematics by the Italian mathematician Leonardo of Pisa, also known as Fibonacci, in his work ‘Liber Abaci’ (Book of Numbers) published in 1202. Fibonacci used this sequence to describe a problem concerning the reproduction of rabbits. Although Fibonacci is the best-known proponent of this sequence, similar numbers have appeared before in the works of Indian mathematicians.

Mathematical properties

The Fibonacci sequence has many interesting mathematical properties. One of these is the ratio of the consecutive numbers, which approaches the golden ratio (phi) of approximately 1.61803. The golden ratio is often considered aesthetically pleasing and appears in many aspects of art and architecture.

Summary

The Fibonacci sequence is not only a mathematical curiosity, but also an important tool in various scientific fields. In the next parts of this series, we will look at how the Fibonacci sequence appears in nature and its applications in marketing and branding.

‍

‍