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Suite de Fibonacci

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 Related:  FibonacciScience

Fibonacci, Carroll, lapin Suite de nombres dont chaque terme est la somme des deux précédents: 11 / 23 ou 23 novembre: jour de Fibonacci (Fibonacci Day). Car la suite de Fibonacci commence par: 1, 1, 2, 3, … Si l'on note Fn la suite de Fibonacci, elle est définie par : Lecture: La suite de Fibonacci Fn est la succession de tous les nombres de n = 1 à l'infini telle que les deux premiers sont égaux à 1 et les suivants se calculent comme la somme des deux précédents. Un tel procédé de définition qui boucle sur lui-même est dit: algorithme de récurrence, ou relation de récurrence ou équation linéaire de récurrence. Voir Démonstration par récurrence

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

How are Fibonacci numbers expressed in nature ­Is there a magic equation to the universe? A series of numbers capable of unraveling the most complicated organic properties or deciphering the plot of "Lost"? Probably not. But thanks to one medieval man's obsession with rabbits, we have a sequence of numbers that reflect various patterns found in nature. ­­­­In 1202, Italian mathematician Leonardo Pisano (also known as Fibonacci, meaning "son of Bonacci") pondered the question: Given optimal conditions, how many pairs of rabbits can be produced from a single pair of rabbits in one year? This thought experiment dictates that the female rabbits always give birth to pairs, and each pair consists of one male and one female. ­Think about it -- two newborn rabbits are placed in a fenced-in yard and left to, well, breed like rabbits. The order goes as follows: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 and on to infinity. At first glance, Fibonacci's experiment might seem to offer little beyond the world of speculative rabbit breeding.

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 . Dans ce code, la séquence « 11 » apparaît uniquement en fin de chaque nombre encodé, et sert ainsi de délimiteur. 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 effectue la somme : 1 + 8 + 21 + 89 = 119 Deuxième exemple

Golden spiral Approximate and true golden spirals: the green spiral is made from quarter-circles tangent to the interior of each square, while the red spiral is a golden spiral, a special type of logarithmic spiral. Overlapping portions appear yellow. The length of the side of a larger square to the next smaller square is in the golden ratio. In geometry, a golden spiral is a logarithmic spiral whose growth factor is φ, the golden ratio.[1] That is, a golden spiral gets wider (or further from its origin) by a factor of φ for every quarter turn it makes. Formula[edit] The polar equation for a golden spiral is the same as for other logarithmic spirals, but with a special value of the growth factor b:[2] or with e being the base of Natural Logarithms, a being an arbitrary positive real constant, and b such that when θ is a right angle (a quarter turn in either direction): Therefore, b is given by The numerical value of b depends on whether the right angle is measured as 90 degrees or as for θ in degrees;

Fibonacci Sequence This sequence is named after the Italian mathematician who lived during the 12th century. It occurs in nature, modelling the population growth in rabbits, and also the development of the spiral in a snail's shell. The terms in the sequence can be made by adding the previous two terms: There is a worksheet here, which can be printed and photocopied for children to use. It involves the children trying to work out how the sequence is made, and then getting them to work out the first 25 numbers in the sequence. These are listed below... The children may want to use a calculator to carry out the latter part of the exercise, but whether they use one or not, they should understand the importance of being accurate (and checking their calculations for errors).

Les retracements de Fibonacci : Analyse technique Vous avez surement un jour entendu parlé de la suite de Fibonacci, rappelez vous : 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 …… Pour les obtenir c’est très simple. Vous additionnez les deux premiers chiffres pour calculer le 3eme. Ainsi 1+1=2 ;1+2=3 ;2+3=5… quelques souvenirs vous reviennent ? Venons en aux nombres d’or maintenant. Les retracements de Fibonacci : Parlons maintenant de ce pourquoi vous êtes venus, les niveaux de retracements de Fibonacci : 23,6%, 38,2%, 50,0%, 61.8%, 100%. - Une tendance haussière est marquée par des phases de corrections - Une tendance baissière est marquée par des phases de rebonds. Ce sont ces corrections ou rebonds qui sont appelés des retracements. Pour déterminer le retracement 50.0% de l'exemple précédent, vous ferez ainsi le calcul suivant : 1.4110 - (0.0100 * 50%) = 1.4060 soit un retracement de 50 pips. Pour le retracement 38.2%, vous ferez le calcul suivant : 1.4110 - (0.0100 * 38.2%) = 1.4072.

Pythagorean Triangles and Triples The calculators on this page require JavaScript but you appear to have switched JavaScript off (it is disabled). Please go to the Preferences for this browser and enable it if you want to use the calculators, then Reload this page. Right-angled triangles with whole number sides have fascinated mathematicians and number enthusiasts since well before 300 BC when Pythagoras wrote about his famous "theorem". The oldest mathematical document in the world, a little slab of clay that would fit in your hand, is a list of such triangles. 1 Right-angled Triangles and Pythagoras' Theorem 1.1 Pythagoras and Pythagoras' Theorem Pythagoras was a mathematician born in Greece in about 570 BC. For example, if the two shorter sides of a right-angled triangle are 2 cm and 3 cm, what is the length of the longest side? 1.2 Some visual proofs of Pythagoras' Theorem My favourite proof of the look-and-see variety is on the right. Both diagrams are of the same size square of side a + b. ) with sides a, b, c. or then

Fabulous Fibonacci Fun! Biographie : Leonardo Fibonacci (1170 [Pise] - 1245 [Pise]) Leonard de Pise, plus connu sous le nom de Fibonacci, est le premier grand mathématicien de l'ère chrétienne du monde occidental. D'assez nombreux détails de sa jeunesse nous sont connus par les propos qu'il tient lui-même dans la préface d'un de ses livres, le Liber abaci. Né à Pise vers 1170, il rejoint très jeune son père à la colonie de Bujania, en Algérie, où ce dernier est responsable du bureau des douanes pour le compte de l'ordre des marchands de Pise. Voulant faire de son fils un marchand, il l'initie à l'art du calcul indo-arabe. Fibonacci apprendra en outre les savoirs et algorithmes orientaux grâce à ses nombreux voyages en Syrie, en Grèce, en Egypte. Fibonacci vivait avant l'invention de l'imprimerie, ce qui signifiait que pour avoir plusieurs exemplaires du même ouvrage, il fallait le travail entièrement manuel d'un copiste. Un autre des plaisirs de l'empereur était les défis mathématiques qu'un membre de sa cour posait à la communauté des scientifiques.

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