# Fibonacci Numbers, the Golden section and the Golden String

Fibonacci Numbers and the Golden Section This is the Home page for Dr Ron Knott's multimedia web site on the Fibonacci numbers, the Golden section and the Golden string hosted by the Mathematics Department of the University of Surrey, UK. The Fibonacci numbers are The golden section numbers are 0·61803 39887... = phi = φ and 1·61803 39887... = Phi = Φ The golden string is 1 0 1 1 0 1 0 1 1 0 1 1 0 1 0 1 1 0 1 ... a sequence of 0s and 1s that is closely related to the Fibonacci numbers and the golden section. If you want a quick introduction then have a look at the first link on the Fibonacci numbers and where they appear in Nature. THIS PAGE is the Menu page linking to other pages at this site on the Fibonacci numbers and related topics above. Fibonacci Numbers and Golden sections in Nature Ron Knott was on Melvyn Bragg's In Our Time on BBC Radio 4, November 29, 2007 when we discussed The Fibonacci Numbers (45 minutes). listen again online or download the podcast. and phi . The Golden Section Related:  Sites

Welcome - OeisWiki NOTE: The Main Page on the OEIS Wiki has much more information (FAQ, Index, Style Sheet, Trouble Logging In, Citations, etc.) Welcome to The On-Line Encyclopedia of Integer Sequences® (OEIS®) Wiki Some Famous Sequences Click on any of the following to see examples of famous sequences in the On-Line Encyclopedia of Integer Sequences (the OEIS), then hit "Back" in your browser to return here: Recamán's sequence, A005132 The Busy Beaver problem, A060843 The Catalan numbers, A000108 The prime numbers, A000040 The Mersenne primes, A000043 and A000668 The Fibonacci numbers, A000045 For some other fascinating sequences see Pictures from the OEIS: The (Free) OEIS Store General Information About OEIS Most people use the OEIS to get information about a particular number sequence. Introductory chapters from the 1973 and 1995 books; Supplement 3 to 1973 book The introductory chapters from N. Description of OEIS entries (or, What is the Next Term?) OEIS: Brief History OEIS: The Movie Index Recent Additions URLs

Fibonacci number A tiling with squares whose side lengths are successive Fibonacci numbers In mathematics, the Fibonacci numbers or Fibonacci sequence are the numbers in the following integer sequence: or (often, in modern usage): (sequence A000045 in OEIS). The Fibonacci spiral: an approximation of the golden spiral created by drawing circular arcs connecting the opposite corners of squares in the Fibonacci tiling;[3] this one uses squares of sizes 1, 1, 2, 3, 5, 8, 13, 21, and 34. By definition, the first two numbers in the Fibonacci sequence are either 1 and 1, or 0 and 1, depending on the chosen starting point of the sequence, and each subsequent number is the sum of the previous two. In mathematical terms, the sequence Fn of Fibonacci numbers is defined by the recurrence relation with seed values or The Fibonacci sequence is named after Fibonacci. Fibonacci numbers are closely related to Lucas numbers in that they are a complementary pair of Lucas sequences. Origins List of Fibonacci numbers and

Interactive Mathematics Miscellany and Puzzles Suite de Fibonacci The Fibonacci Sequence is the series of numbers: The next number is found by adding up the two numbers before it. The 2 is found by adding the two numbers before it (1+1) Similarly, the 3 is found by adding the two numbers before it (1+2), And the 5 is (2+3), and so on! Example: the next number in the sequence above is 21+34 = 55 It is that simple! Here is a longer list: Can you figure out the next few numbers? Makes A Spiral When we make squares with those widths, we get a nice spiral: Do you see how the squares fit neatly together? The Rule The Fibonacci Sequence can be written as a "Rule" (see Sequences and Series). First, the terms are numbered from 0 onwards like this: So term number 6 is called x6 (which equals 8). So we can write the rule: The Rule is xn = xn-1 + xn-2 where: xn is term number "n" xn-1 is the previous term (n-1) xn-2 is the term before that (n-2) Example: term 9 is calculated like this: Golden Ratio And here is a surprise. Using The Golden Ratio to Calculate Fibonacci Numbers

Home Page Teachers Primary Pupils Secondary Students Events and PD "It gave me some good ideas to use in the classroom and ... a link that I can get all of the activities from." Book NRICH Bespoke PDBook Forthcoming EventsBook our Hands-on Roadshow Your Solutions Codage de Fibonacci Un article de Wikipédia, l'encyclopédie libre. Le codage de Fibonacci est un codage entropique utilisé essentiellement en compression de données . Il utilise les nombres de la suite de Fibonacci , dont les termes ont la particularité d'être composés de la somme des deux termes consécutifs précédents, ce qui lui confère une robustesse aux erreurs. Le code de Fibonacci produit est un code préfixe et universel . Principe [ modifier ] Codage [ modifier ] Pour encoder un entier X : Créer un tableau avec 2 lignes. Exemple décomposition de 50. Les éléments de la 1 re ligne du tableau sont : 1 2 3 5 8 13 21 34 50 = 34 + 13 + 3 (50 = 34 + 8 + 5 + 3 est incorrect car le 13 n'a pas été utilisé) D'où le tableau : Il reste à écrire le codage du nombre 50 : 001001011 Décodage [ modifier ] Premier exemple Décoder le nombre 10001010011 On enlève le dernier "1" puis on reporte les "0" et les "1" restants dans le tableau suivant : On effectue la somme : 1 + 8 + 21 + 89 = 119 Deuxième exemple Décoder le nombre 1011001111

BASE Cinque light - Appunti di Matematica ricreativa BASE Cinque in Power-Saving Mode Cari amici, BASE Cinque ha bisogno di riposare un po'. Per un periodo imprecisato di tempo non inserirò nuovi articoli. Il sito tuttavia rimane attivo e tutti i suoi contenuti sono raggiungibili consultando l'archivio o il motore di ricerca interno. Se avete un problema interessante o divertente, non esitate: inviatelo al forum. Pace e bene a tutti! Appunti precedenti Il diario di BASE Cinque - 2015 Il diario di BASE Cinque - 2014 Il diario di BASE Cinque - 2013 Il diario di BASE Cinque - 2012 Il diario di BASE Cinque - 2011 Il diario di BASE Cinque - 2010 Il diario di BASE Cinque - 2009 Il diario di BASE Cinque - 2008 Il diario di BASE Cinque - 2007 Degli anni 2005 e 2006 non esiste il diario. Ricreazioni ricevute 2000 - 2004

The Fibonacci Numbers and Golden section in Nature - 1 This page has been split into TWO PARTS. This, the first, looks at the Fibonacci numbers and why they appear in various "family trees" and patterns of spirals of leaves and seeds. The second page then examines why the golden section is used by nature in some detail, including animations of growing plants. 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987 ..More.. 1 Rabbits, Cows and Bees Family Trees Let's look first at the Rabbit Puzzle that Fibonacci wrote about and then at two adaptations of it to make it more realistic. 1.1 Fibonacci's Rabbits The original problem that Fibonacci investigated (in the year 1202) was about how fast rabbits could breed in ideal circumstances. Suppose a newly-born pair of rabbits, one male, one female, are put in a field. How many pairs will there be in one year? At the end of the first month, they mate, but there is still one only 1 pair. The number of pairs of rabbits in the field at the start of each month is 1, 1, 2, 3, 5, 8, 13, 21, 34, ...

LessThan3Math Vediamo cosa sono le proporzioni e come fare a trovare il termine incognito. Parleremo inoltre delle proprietà delle proporzioni e vedremo alcuni esempi di problemi risolvibili con proporzioni 😉 Le proporzioni si incontrano la prima volta alle scuole medie ma capita di utilizzarle frequentemente anche alle scuole superiori. Le principali proprietà delle proporzioni di cui parleremo sono la proprietà fondamentale, la proprietà del permutare, la proprietà del comporre, la proprietà dello scomporre e la proprietà dell'invertire. Trovi altri video su proporzioni e percentuali nella playlist✔ Follow me on Facebook & Instagram, it's the cool thing to do these days ;)✔ Informazioni sulle videolezioni ed elenco completo✔ L'attrezzatura in cui ho investito per creare i video✔ Grazie a tutti per i MI PIACE, le ISCRIZIONI ed i COMMENTI =)

Suite de Fibonacci Un article de Wikipédia, l'encyclopédie libre. Elle doit son nom à Leonardo Fibonacci qui, dans un problème récréatif posé dans l'ouvrage Liber abaci publié en 1202, décrit la croissance d'une population de lapins : « Un homme met un couple de lapins dans un lieu isolé de tous les côtés par un mur. Combien de couples obtient-on en un an si chaque couple engendre tous les mois un nouveau couple à compter du troisième mois de son existence ? » Cette suite est fortement liée au nombre d'or, φ (phi). Croissance de population des lapins selon une suite de Fibonacci Présentation mathématique[modifier | modifier le code] Formule de récurrence[modifier | modifier le code] Le problème de Fibonacci est à l'origine de la suite dont le -ième terme correspond au nombre de paires de lapins au -ème mois. Notons le nombre de couples de lapins au début du mois . Dès le début du troisième mois, le couple de lapins a deux mois et il engendre un autre couple de lapins ; on note alors Plaçons-nous maintenant au mois

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