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The Fibonacci Numbers and Golden section in Nature - 1

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, ... Related:  mathematics

Chaos & Fractals Chaos is a relatively new and exciting science. Although chaos was often unfavorably viewed its early stages, scientists now perform active research in many areas of the field. Presently, there are several journals dedicated solely to the study of chaos. This website was written in conjunction with a talk given for Intermediate Physics Seminar of the Department of Physics and Astronomy at the Johns Hopkins University. It is intended to merely highlight a few of the more interesting aspects in the field of chaos. For further information, please consult the reference section of this document.

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. Le nombre d’or est le rapport entre deux chiffres compris dans cette suite. Tout d’abord on calcule le ratio entre un nombre et son suivant par exemple, 89/144=0.618. 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 le retracement 38.2%, vous ferez le calcul suivant : 1.4110 - (0.0100 * 38.2%) = 1.4072.

What’s the Difference Between a MOOC and an LMS? | Your Training Edge ® Massive open online courses (MOOCs) have been around long enough that most people in the training industry have at least a general understanding of what they are. But there is still some confusion about how they differ from more familiar forms of elearning and online courses. In particular, a question I’m often asked is: “What’s the difference between a MOOC and a learning management system (LMS)?” The basic answer is that an LMS is a platform for hosting a course, while a MOOC is the course itself. In general, however, I don’t think the real question is about the difference between a MOOC as a course and an LMS as a platform. Small versus large (or massive) In theory MOOCs can accommodate an unlimited number of learners. Discrete versus continuous Traditional courses hosted on LMSs are usually discrete entities, meaning that that they start on a particular day, end on a particular day, have particular due dates, and so on. Content versus context This is a common distinction that is made.

Probability Central Main Page As of July 1, 2013 ThinkQuest has been discontinued. We would like to thank everyone for being a part of the ThinkQuest global community: Students - For your limitless creativity and innovation, which inspires us all. Teachers - For your passion in guiding students on their quest. Partners - For your unwavering support and evangelism. Parents - For supporting the use of technology not only as an instrument of learning, but as a means of creating knowledge. We encourage everyone to continue to “Think, Create and Collaborate,” unleashing the power of technology to teach, share, and inspire. Best wishes, The Oracle Education Foundation

library.thinkquest.org/3703/ As of July 1, 2013 ThinkQuest has been discontinued. We would like to thank everyone for being a part of the ThinkQuest global community: Students - For your limitless creativity and innovation, which inspires us all. Teachers - For your passion in guiding students on their quest. Partners - For your unwavering support and evangelism. Parents - For supporting the use of technology not only as an instrument of learning, but as a means of creating knowledge. We encourage everyone to continue to “Think, Create and Collaborate,” unleashing the power of technology to teach, share, and inspire. Best wishes, The Oracle Education Foundation 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

Kidspiration - The Visual Way to Explore Words, Numbers and Concepts Created for primary learners, Kidspiration® develops literacy, numeracy and thinking skills using proven visual learning principles. In literacy, Kidspiration strengthens word recognition, vocabulary, comprehension and written expression. With new visual maths tools, students build reasoning and problem-solving skills. Kidspiration helps pupils: Develop strong thinking skills Strengthen literacy skills Build conceptual understanding in maths Develop Strong Thinking SkillsStrengthen Literacy SkillsBuild Conceptual Understanding in MathsEducator Developed Resources Support Curriculum IntegrationEasy Navigation and Simple Operations Support for Every Primary LearnerTeacher Options Keep Pupils Focused on LearningSupport for ELL and ESL StudentsKidspiration Keeps Up with the Latest Technology Kidspiration provides a cross-curricular visual workspace for primary learners. Kidspiration works the way pupils think and learn and the way teachers teach. Develop Strong Thinking Skills

Golden ratio Line segments in the golden ratio In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. The figure on the right illustrates the geometric relationship. Expressed algebraically, for quantities a and b with a > b > 0, The golden ratio is also called the golden section (Latin: sectio aurea) or golden mean.[1][2][3] Other names include extreme and mean ratio,[4] medial section, divine proportion, divine section (Latin: sectio divina), golden proportion, golden cut,[5] and golden number.[6][7][8] Some twentieth-century artists and architects, including Le Corbusier and Dalí, have proportioned their works to approximate the golden ratio—especially in the form of the golden rectangle, in which the ratio of the longer side to the shorter is the golden ratio—believing this proportion to be aesthetically pleasing (see Applications and observations below). Calculation Therefore, Multiplying by φ gives and History

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

Interactive Mathematics Miscellany <br>and Puzzles

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