Decay of geometry for Fibonacci critical covering maps of the circle

We study the growth of Df `` (f(c)) when f is a Fibonacci critical covering map of the circle with negative Schwarzian derivative, degree d >= 2 and critical point c of order l > 1. As an application we prove that f exhibits exponential decay of geometry if and only if l <= 2, and in this case it has an absolutely continuous invariant probability measure, although not satisfying the so-called Collet-Eckmann condition. (C) 2009 Elsevier Masson SAS. All rights reserved.

Fibonacci bimodal maps

We introduce the Fibonacci bimodal maps on the interval and show that their two turning points are both in the same minimal invariant Cantor set. Two of these maps with the same orientation have the same kneading sequences and, among bimodal maps without central returns, they exhibit turning points with the strongest recurrence as possible.

EIGENVALUES of FIBONACCI STOCHASTIC ADDING MACHINE

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Band edge states of the < n >=0 gap of Fibonacci photonic lattices

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Deficient generalized Fibonacci maximum path graphs /

"UILU-ENG 78 1739."

Иновации в математическото образование: европейските проекти InnoMathEd и Fibonacci

Petar Kenderov The paper considers the participation of the Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences, into two European projects, InnoMathEd and Fibonacci. Both projects address substantial innovations in mathematics education and their dissemination on European level. Inquiry based learning is the central focus of the two projects. A special emphasis is paid on the outcomes of the projects in terms of didactic concepts, pedagogical methodologies and innovative learning environments aimed at pupils’ active, self-responsible and exploratory learning.

Fibonacci Series, Golden Proportions, and the Human Biology

Pythagoras, Plato and Euclid’s paved the way for Classical Geometry. The idea of shapes that can be mathematically defined by equations led to the creation of great structures of modern and ancient civilizations, and milestones in mathematics and science. However, classical geometry fails to explain the complexity of non-linear shapes replete in nature such as the curvature of a flower or the wings of a Butterfly. Such non-linearity can be explained by fractal geometry which creates shapes that emulate those found in nature with remarkable accuracy. Such phenomenon begs the question of architectural origin for biological existence within the universe. While the concept of a unifying equation of life has yet to be discovered, the Fibonacci sequence may establish an origin for such a development. The observation of the Fibonacci sequence is existent in almost all aspects of life ranging from the leaves of a fern tree, architecture, and even paintings, makes it highly unlikely to be a stochastic phenomenon. Despite its wide-spread occurrence and existence, the Fibonacci series and the Rule of Golden Proportions has not been widely documented in the human body. This paper serves to review the observed documentation of the Fibonacci sequence in the human body.

Sequências de Fibonacci e a Razão Áurea - aplicações no ensino básico

This thesis aims to present a study of the Fibonacci sequence, initiated from a simple problem of rabbits breeding and the Golden Ratio, which originated from a geometrical construction, for applications in basic education. The main idea of the thesis is to present historical records of the occurrence of these concepts in nature and science and their influence on social, cultural and scientific environments. Also, it will be presented the identification and the characterization of the basic properties of these concepts and howthe connection between them occurs,and mainly, their intriguing consequences. It is also shown some activities emphasizing geometric constructions, links to other mathematics areas, curiosities related to these concepts and the analysis of questions present in vestibular (SAT-Scholastic Aptitude Test) and Enem(national high school Exam) in order to show the importance of these themes in basic education, constituting an excellent opportunity to awaken the students to new points of view in the field of science and life, from the presented subject and to promote new ways of thinking mathematics as a transformative science of society.

Successione di Fibonacci e applicazioni

Nella tesi descrivo la successione di Fibonacci che è la più antica fra le successioni ricorsive note e nasce da un semplice quesito sulla riproduzione dei conigli. Inoltre introduco alcune proprietà e caratteristiche dei numeri che la compongono tra cui, la principale, la sezione aurea. Negli ultimi capitoli espongo le applicazioni di questi numeri in natura e introduco la definizione di terna pitagorica per enunciare teoremi che collegano i numeri di Fibonacci con l'ipotenusa dei triangoli rettangoli.