![]() Here's an iterative algorithm for printing the Fibonacci sequence: Recursion, on the other hand, means performing a single task and proceeding to the next for performing the remaining task. Iteration means repeating the work until the specified condition is met. You can write a computer program for printing the Fibonacci sequence in 2 different ways: ![]() ![]() How to Print the Fibonacci Sequence in Python Leonardo was known as one of the most talented mathematicians of the middle ages. He was from the Republic of Pisa, which is why he is also known as Leonardo of Pisa. This fascinating sequence is widely associated with the mathematician Leonardo Pisano, also known as Fibonacci. We can use this sequence to find any nth Fibonacci number. Mathematically, the Fibonacci Sequence is represented by this formula: Within this continuous sequence, every individual number is a Fibonacci number. Here's a diagram showing the first 10 Fibonacci numbers: Similarly, the next Fibonacci number is - 0, 1, 1, (2). We can represent this more mathematically like 0, 1, (1). Then, to find the next number, you add the last number you have and the number before it. They're the first two numbers in the sequence. Then every following number is made up of adding the previous two numbers together.įor example, take 0 and 1. The Fibonacci sequence starts with two numbers, that is 0 and 1. And adding the previous 2 numbers some number of times forms a series that we call the Fibonacci Series. The Fibonacci Sequence is a sequence of numbers in which a given number is the result of adding the 2 numbers that come before it. In this article, I'll explain a step-by-step approach on how to print the Fibonacci sequence using two different techniques, iteration and recursion.īefore we begin, let's first understand some basic terminology. ![]() Leonardo has been called ‘Fibonacci’ ever since.Questions about the Fibonacci Series are some of the most commonly asked in Python interviews. In the 1870s, the French mathematician Edouard Lucas assigned the name “Fibonacci” to the number sequence that is the solution to the famous “Rabbit Problem” in Leonardo Pisano’s book, Liber Abaci (1228). Remarkably, it was yet another hundred years before Leonardo would once again be acknowledged academically and given the credit to which he is due. This was in 1797, over five centuries after Leonardo had died. This remarkable endorsement did not resuscitate Leonardo’s legacy, however, and his name was once more quickly forgotten.įor another three hundred years historical anonymity obscured the achievements of Leonardo Pisano until one day, by slim chance, a mathematics historian named Pietro Cossali (1748-1815) noticed Pacioli’s reference and began researching Leonardo’s works on his own. No biographies were written about him or his many accomplishments in math even mathematicians did not know who he was until 1494, when a respected Italian mathematician named Luca Pacioli (1447-1517) briefly mentioned Leonardo’s name in the introduction to a book of his own, Summa, giving credit to him for most of the ideas presented in his own book. Master Leonardo Pisano (not to be confused with Leonardo da Vinci) was a beloved public servant of Pisa, Italy, who achieved fame during his lifetime (ca.1170 – ca.1250) but was forgotten within two hundred years. The formula for Golden Ratio is: F(n) = (x^n – (1-x)^n)/(x – (1-x)) where x = (1+sqrt 5)/2 ~ 1.618 The Golden Ratio represents a fundamental mathematical structure which appears prevalent – some say ubiquitous – throughout Nature, especially in organisms in the botanical and zoological kingdoms. Phi and phi are also known as the Golden Number and the Golden Section. CB/AC – is the same as the ratio of the larger part, AC, to the whole line AB. In the image below, the ratio of the smaller part of a line (CB), to the larger part (AC) – i.e. Phi (Φ), 1.61803 39887…, is also the number derived when you divide a line in mean and extreme ratio, then divide the whole line by the largest mean section its inverse is phi (φ), 0.61803 39887…, obtained when dividing the extreme (smaller) portion of a line by the (larger) mean. After these first ten ratios, the quotients draw ever closer to Phi and appear to converge upon it, but never quite reach it because it is an irrational number. When a number in the Fibonacci series is divided by the number preceding it, the quotients themselves become a series that follows a fascinating pattern: 1/1 = 1, 2/1 = 2, 3/2 = 1.5, 5/3 = 1.666…, 8/5 = 1.6, 13/8 = 1.625, 21/13 = 1.61538, 34/21 = 1.619, 55/34 = 1.6176…, and 89/55 = 1.618… The first ten ratios approach the numerical value 1.618034… which is called the “Golden Ratio” or the “Golden Number,” represented by the Greek letter Phi (Φ, φ). Related to the Fibonacci sequence is another famous mathematic term: the Golden Ratio.
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