The Fibonacci Sequence

FIBONACCI… questo è italiano!

Hey guys! I’m back again with some fresh terminology that would probably bring some concerns… Anyways, no time for intrigues, we have no time to spare! The first question many of you may ask would be:


for goodness’ sake, why come up with such a name for a math concept???

Alright, so the reason for bearing such an unusual name might be because the initiator’s name was so! Sounds simple, doesn’t it? Well, hold on for dessert.

Leonard of Pisa (Fibonacci)

Fibonacci (1170-1250 A.E.) was born in Italy but obtained his education in North Africa. Very little is known about him or his family and there are no photographs or drawings of him. Much of the information about Fibonacci has been gathered by his autobiographical notes which he included in his books.

However, Fibonacci is considered to be one of the most talented mathematicians of the Middle Ages. Few people realize that it was Fibonacci that gave us our decimal number system (Hindu-Arabic numbering system) which replaced the Roman Numeral system. When he was studying mathematics, he used the Hindu-Arabic (0-9) symbols instead of Roman symbols which didn’t have 0’s and lacked place value. In fact, when using the Roman Numeral system, an abacus was usually required. There is no doubt that Fibonacci saw the superiority of using Hindu-Arabic system over the Roman Numerals. He shows how to use our current numbering system in his book “Liber abaci”.


Despite his ‘unknown’ life story, he is mostly famous for his valuable contributions to number theory:

  • In his book, “Liber Abbaci,” he introduced the Hindu-Arabic place-valued decimal system and the use of Arabic numerals into Europe:

Image result for Liber Abaci

  • He introduced us to the bar we use in fractions, previous to this, the numerator has quotations around it.Image result for fractions fibonacci
  • The square root notation is also a Fibonacci method.Image result for square root memes

WHAT DOes this have to do with the “sequence”?

According to Barron’s Standardized Test book, a “Sequence” is…

…a function with a domain consisting of the natural numbers. Whilst a “Series” is the sum of the terms of a sequence.


In other words, a sequence is are consecutive numbers going one after another, up to a specific number or infinity (recall to your Algebra 1 (2) classes where the “geometric and arithmetic sequences” were utilized). For example, I say I bought 1, 2, 3, 4, 5, 6 apples. Albeit, Karim counted off 1, 2, 4, 16 products from the grocery store. Get the difference now? Thus, let’s get closer to the plot.


The Fibonacci sequence is a series of numbers where a number is found by adding up the two numbers before it. Starting with 0 and 1, the sequence goes 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and so forth. Written as a rule, the expression is xn = xn-1 + xn-2.

Fibonacci first noted the sequence when pondering a mathematical problem about rabbit breeding. Beginning with a male and female rabbit, how many pairs of rabbits could be born in a year? The problem assumes the following conditions:

  • Begin with one male rabbit and female rabbit that have just been born.
  • Rabbits reach sexual maturity after one month.
  • The gestation period of a rabbit is one month.
  • After reaching sexual maturity, female rabbits give birth every month.
  • A female rabbit gives birth to one male rabbit and one female rabbit.
  • Rabbits do not die.

After one month, the first pair is not yet at sexual maturity and can’t mate. At two months, the rabbits have mated but not yet given birth, resulting in only one pair of rabbits. After three months, the first pair will give birth to another pair, resulting in two pairs. At the fourth month mark, the original pair gives birth again, and the second pair mates but does not yet give birth, leaving the total at three pair. This continues until a year has passed, in which there will be 233 pairs of rabbits.

Oh come on, this can’t be better than officer hops from
“zootopia”… Where’s the dessert?

Although the Fibonacci sequence was presented in a fairly biological, it is implemented by nature in a variety of flowers and animals.

In sunflowers, for instance

This phenomena is mostly called as the:

Fibonacci Spiral

A Fibonacci spiral is a series of connected quarter-circles drawn inside an array of squares with Fibonacci numbers for dimensions. The squares fit perfectly together because of the nature of the sequence, where the next number is equal to the sum of the two before it. Any two successive Fibonacci numbers have a ratio very close to the Golden Ratio, which is roughly 1.618034. The larger the pair of Fibonacci numbers, the closer the approximation. The spiral and resulting rectangle are known as the Golden Rectangle. It was mostly used during the illustration of the famous Mona Lisa and other Renaissance art works.

BUON APPETITO AMICI MIEI!


That was all for today my fellow readers, hope you liked it as much as I did!

Feel free to leave some comments below in case of some flaws you might’ve noticed while reading this article and see you next time!

 

 

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Written by Shohruh Artaman
A typical writer illustrating typical principles
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2 комментария
  1. Well done

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  2. Shohruh, good job! Very interesting article!

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