background preloader

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

Biographie de Edouard Lucas Edouard Lucas est un arithméticien français également connu pour ses Récréations mathématiques. Enfant issu d'une famille très modeste (son père est artisan tonnelier à Amiens), il reçoit une bourse communale et réussit le concours d'entrée à l'Ecole Normale Supérieure, en 1861 (année de la promotion de Gaston Darboux, qui sera le seul à le précéder à l'Agrégation quelques années plus tard!). A la sortie de l'Ecole, il devient astronome adjoint à l'Observatoire de Paris, puis après la guerre franco-prussienne, il obtient une chaire de Mathématiques Spéciales à Moulins, de 1872 à 1876, où il épousera en août 1873 Marthe Boyron. Puis il occupe une chaire à Paris, d'abord au lycée Charlemagne à Paris, puis au déjà très prestigieux lycée Saint-Louis. Ses travaux mathématiques concernent la géométrie euclidienne non élémentaire (celle des transformations, en particulier la géométrie projective vue à travers ses homographies), et surtout la théorie des nombres.

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.

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.

coefficients binomiaux et la suite de Fibonacci / Café mathématique / Forum de mathématiques Salut, Non, décidément, ton idée de gens qui savent et ne veulent rien dire, n'a pas de sens, cela confine à la paranoïa...La formulation des coefficients binomiaux, comme des Arrangements et Combinaisons est donnée en Terminale...D'accord ?Et les Maths ne s'arrêtent pas à la Terminale...Or, que trouve-t-on, entre autres, sur BibMath ?Tout simplement ceci : un dictionnaire de Maths...Et si tu le feuillettes, tu t'apercevras qu'il regorge de notions très pointues qui dépassent de loin le niveau Terminale...Mais ce que tu cherches ne s'y trouve pas !D'accord ?Alors, comment ton affirmation peut-elle être compatible avec ce fait ? la premiere est qu'un savoir maths est dependant d'un niveau scolaire:celui qui aide fait cela en tant que pédagogue afin que l'on avance dans les mathssi on lui demande telle ou telle formule qu'il connait il ne verra pas l'interêt pédagogique de la donner celui qui aide fait cela en tant que pédagogue afin que l'on avance dans les maths Vale tibi !

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 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

Suite de Fibonacci Ce site utilise des cookies pour faciliter votre navigation, obtenir des statistiques de visite, et afficher des publicités personnalisées. En savoir plus Enfermez un couple de lapins dans un enclos. Le premier mois de leur vie, il n'ont pas d'enfants. Il se trouve que l'on rencontre très souvent ces nombres dans la nature, par exemple en observant une fleur de tournesol, ou certains coquillages. Consulter aussi...

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

Interactive Mathematics Miscellany <br>and Puzzles Suite de Lucas, cousine de Fibonacci Les nombres tétranacci commencent par 0, 0, 0, 1 et se poursuivent en ajoutant les quatre termes précédents: Les nombres pentanacci: Liste de tous les nombres de Fibonacci à pentanacci

Related: