# Fibonacci Number/Sequence

Mind Map by Andrea Leyden, updated more than 1 year ago More Less
 Created by samuel.cook over 5 years ago Copied by Andrea Leyden over 5 years ago
856
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### Description

This Mind Map gives an overview of the Fibonacci numbers or Fibonacci sequence for GCSE Algebra.

## Resource summary

Fibonacci Number/Sequence
1 Question Number 1
1.1 Can you identify if a number is a fibonacci number when you see it on its own?
1.1.1 Yes there is a way
1.1.1.1 You can test it using a formula.
1.1.1.1.1 If the square root of 5(n*)-4 or 5(n*)+4 is a whole number (a perfect square) then the number is a Fibonacci number.
1.1.1.1.1.1 *= squared; n= the number
2 Question Number 2
2.1 Is there a formula to calculate the next Fibonacci number when you are given a single Fibonacci number?
2.1.1 The ratio of any Fibonacci number with the previous Fibonacci number is a consistent ratio.
2.1.1.1 This ratio is known as the golden ratio which is about 1.631803
2.1.1.1.1 So if you multiply any Fibonacci number by the golden ratio you will obtain the next Fibonacci number.
3 Facts about Fibonacci
3.1 Born: 1170 in (probably) Pisa (now in Italy) Died: 1250 in (possibly) Pisa (now in Italy)
3.2 His real name was Leonardo Pisano
3.3 There is now a statue commemorating him located at the Leaning Tower end of the cemetery next to the Cathedral in Pisa.
4 How the fibonacci sequence appears in our lives.
4.1 The Fibonacci sequence plays a small part in the bestselling novel and film The Da Vinci Code
4.2 In the February 8, 2009 edition of FoxTrot by Bill Amend, characters Jason and Marcus take one nacho from a bowl, one more nacho, then two nachos, three nachos, five nachos, eight nachos, etc., calling it 'Fibonacho.'
4.3 Artist Mario Merz made the Fibonacci sequence a recurring theme in his work. Examples are the Chimney of Turku Energia, in Turku, Finland, featuring the start of the Fibonacci sequence in 2m high neon lights.
4.4 Fibonacci numbers have also been used in knitting to create aesthetically appealing patterns.
4.5 The full grown middle finger length uses the Fibonacci sequence
4.6 As well as the representation of the first Fibonacci numbers with red neon lights on one of the four-faced dome of the Mole Antonelliana in Turin, Italy, part of the artistic work Il volo dei Numeri ("Flight of the numbers").
5 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377....

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