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Author: Boris Rozin Publisher: BrownWalker Press ISBN: 1627347488 Category : Science Languages : en Pages : 186
Book Description
This book is devoted to anyone who is in search of beauty in mathematics, and mathematics in the beauty around us. Attempting to combine mathematical rigor and magnificence of the visual perception, the author is presenting the mathematical study of phyllotaxis, the most beautiful phenomenon of the living nature. The distinctive feature of this book is an animation feature that explains the work of mathematical models and the transformation of 3D space. The analysis of the phyllotactic pattern as a system of discrete objects together with the mathematical tools of generalized sequences made it possible to find a universal algorithm for calculating the divergence angle. In addition, it is serving as a new proof of the fundamental theorem of phyllotaxis and analytically confirming well-known formulas obtained intuitively earlier as well as casting some doubts on a few stereotypes existing in mathematical phyllotaxis. The presentation of phyllotaxis morphogenesis as a recursive process allowed the author to formulate the hydraulic model of phyllotaxis morphogenesis and propose a method for its experimental verification. With the help of artificial intelligence, the author offered methodology for the digital measurement of phyllotaxis allowing a transition to a qualitatively new level in the study of plant morphogenesis. Due to the successful combination of mathematical constructions and their visual presentation, the materials of this study are comprehensible to readers with high school advanced mathematical levels.
Author: Boris Rozin Publisher: BrownWalker Press ISBN: 1627347488 Category : Science Languages : en Pages : 186
Book Description
This book is devoted to anyone who is in search of beauty in mathematics, and mathematics in the beauty around us. Attempting to combine mathematical rigor and magnificence of the visual perception, the author is presenting the mathematical study of phyllotaxis, the most beautiful phenomenon of the living nature. The distinctive feature of this book is an animation feature that explains the work of mathematical models and the transformation of 3D space. The analysis of the phyllotactic pattern as a system of discrete objects together with the mathematical tools of generalized sequences made it possible to find a universal algorithm for calculating the divergence angle. In addition, it is serving as a new proof of the fundamental theorem of phyllotaxis and analytically confirming well-known formulas obtained intuitively earlier as well as casting some doubts on a few stereotypes existing in mathematical phyllotaxis. The presentation of phyllotaxis morphogenesis as a recursive process allowed the author to formulate the hydraulic model of phyllotaxis morphogenesis and propose a method for its experimental verification. With the help of artificial intelligence, the author offered methodology for the digital measurement of phyllotaxis allowing a transition to a qualitatively new level in the study of plant morphogenesis. Due to the successful combination of mathematical constructions and their visual presentation, the materials of this study are comprehensible to readers with high school advanced mathematical levels.
Author: Denis Barabe Publisher: World Scientific ISBN: 9811211027 Category : Science Languages : en Pages : 298
Book Description
The book provides a current review of the field of phyllotaxis from a variety of perspectives, that is, morphological, developmental, biochemical, molecular genetics, biophysical, and evolutionary.This unique book covers phyllotactic processes from the level of genes involved in the establishment of patterns to modeling the emergence of those patterns in space and time. The models in question (deterministic or stochastic) touch on various fields, including geometry, biochemistry, and biophysics.Not only providing a recent review but also current critique and analysis of the discipline, the book will appeal to a variety of individuals involved in developmental modeling as well as pattern initiation and formation. The text is highly illustrated with excellent pictures representing recent developments in the field.A biological context or perspective to models and ideas is explored in the book. Terminology specific to the discipline is defined and updated as well.
Author: Roger V. Jean Publisher: World Scientific ISBN: 9789810226213 Category : Science Languages : en Pages : 900
Book Description
The book deals with biological, mathematical, descriptive, causal and systemic phyllotaxis. It aims at reflecting the widest possible range of ideas and research closely related to phyllotaxis and contains 30 well illustrated chapters.The book has three parts of equal importance. The first two parts concern data collecting, pattern recognition and pattern generation to which students of phyllotaxis are well accustomed. The third part is devoted to the problem of origins of phyllotactic patterns, giving the field of phyllotaxis the universality it requires to be fully understood.Phyllotaxis-like patterns are found in places where genes are not necessarily present. Part III concerns general comparative morphology, homologies with phyllotactic patterns, and recent trends on evolution that can help to understand phyllotaxis.The distinguished researchers who accepted to participate in the production of this book, strongly contributed to the field of phyllotaxis in the past and have devoted a lot of their time to the fascinating subject coming up with most valuable findings, or are newcomers with original ideas that may be very relevant for the future of the field. The book summarizes and updates their contributions, and promotes new avenues in the treatment of phyllotaxis.This book on mathematical and biological phyllotaxis is the first collective book ever. A landmark in the history of phyllotaxis.
Author: Irving Adler Publisher: World Scientific Publishing Company Incorporated ISBN: 9789814407625 Category : Mathematics Languages : en Pages : 205
Book Description
Foreword by Stephen L Adler (Institute for Advanced Study, USA) Illustrations by Peggy Adler The term Phyllotaxis refers to the patterns on plants formed by the arrangement of repeated biological units. In nearly all cases, the Fibonacci Numbers and the Golden Ratio occur in these arrangements. This topic has long fascinated scientists. Over a period of more than two decades, Irving Adler wrote a number of papers that construct a rigorously derived mathematical model for Phyllotaxis, which are major and enduring contributions to the field. These papers are collected in this reprint volume to enable their access to a wider readership.
Author: Douglas Soltis Publisher: University of Chicago Press ISBN: 022644175X Category : Science Languages : en Pages : 587
Book Description
Although they are relative latecomers on the evolutionary scene, having emerged only 135?170 million years ago, angiosperms—or flowering plants—are the most diverse and species-rich group of seed-producing land plants, comprising more than 15,000 genera and over 350,000 species. Not only are they a model group for studying the patterns and processes of evolutionary diversification, they also play major roles in our economy, diet, and courtship rituals, producing our fruits, legumes, and grains, not to mention the flowers in our Valentine’s bouquets. They are also crucial ecologically, dominating most terrestrial and some aquatic landscapes. This fully revised edition of Phylogeny and Evolution of the Angiosperms provides an up-to-date, comprehensive overview of the evolution of and relationships among these vital plants. Incorporating molecular phylogenetics with morphological, chemical, developmental, and paleobotanical data, as well as presenting a more detailed account of early angiosperm fossils and important fossil information for each evolutionary branch of the angiosperms, the new edition integrates fossil evidence into a robust phylogenetic framework. Featuring a wealth of new color images, this highly synthetic work further reevaluates long-held evolutionary hypotheses related to flowering plants and will be an essential reference for botanists, plant systematists, and evolutionary biologists alike.
Author: Alexey Stakhov Publisher: World Scientific ISBN: 9812775838 Category : Mathematics Languages : en Pages : 745
Book Description
Assisted by Scott Olsen ( Central Florida Community College, USA ). This volume is a result of the author's four decades of research in the field of Fibonacci numbers and the Golden Section and their applications. It provides a broad introduction to the fascinating and beautiful subject of the OC Mathematics of Harmony, OCO a new interdisciplinary direction of modern science. This direction has its origins in OC The ElementsOCO of Euclid and has many unexpected applications in contemporary mathematics (a new approach to a history of mathematics, the generalized Fibonacci numbers and the generalized golden proportions, the OC goldenOCO algebraic equations, the generalized Binet formulas, Fibonacci and OC goldenOCO matrices), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational radices, Fibonacci computers, ternary mirror-symmetrical arithmetic, a new theory of coding and cryptography based on the Fibonacci and OC goldenOCO matrices). The book is intended for a wide audience including mathematics teachers of high schools, students of colleges and universities and scientists in the field of mathematics, theoretical physics and computer science. The book may be used as an advanced textbook by graduate students and even ambitious undergraduates in mathematics and computer science. Sample Chapter(s). Introduction (503k). Chapter 1: The Golden Section (2,459k). Contents: Classical Golden Mean, Fibonacci Numbers, and Platonic Solids: The Golden Section; Fibonacci and Lucas Numbers; Regular Polyhedrons; Mathematics of Harmony: Generalizations of Fibonacci Numbers and the Golden Mean; Hyperbolic Fibonacci and Lucas Functions; Fibonacci and Golden Matrices; Application in Computer Science: Algorithmic Measurement Theory; Fibonacci Computers; Codes of the Golden Proportion; Ternary Mirror-Symmetrical Arithmetic; A New Coding Theory Based on a Matrix Approach. Readership: Researchers, teachers and students in mathematics (especially those interested in the Golden Section and Fibonacci numbers), theoretical physics and computer science."
Author: Bir Bahadur Publisher: CRC Press ISBN: 0429960700 Category : Nature Languages : en Pages : 370
Book Description
Plants exhibit forms of asymmetry analogous to "handedness" in bilaterally symmetrical animals. This book explores the evolutionary significance and development of asymmetry. Examples of genetic control include the direction of tendril or stem coiling of many climbing plants; the so-called spiral phyllotaxy and floral taxy; and contorted petal arrangement is another kind of left- right symmetry in plants; the direction of contortion is fixed in some but not in other plants. The book will underscore tha all phenomena related to handedness start during embryogenesis itself, with the occurrence of embryo rotation. Key selling features: First consolidated book on Plant Handedness Relates handedness, asymmetry and chirality to the evolution of different organizational levels in plant biology Emphasizes handedness as a vital governing force in plant functional evolution Provides a new perspective, hitherto ignored, into plant developemtn and evolution Describes how an age-old phenomenon can give scope for investigation from a very modern interdisciplinary approach
Author: Boris Rozin
Author: Boris Rozin
Author: Arthur Harry Church
Author: Arthur Harry Church
Author: Denis Barabe
Author: Roger V. Jean
Author: Irving Adler
Author: Douglas Soltis
Author: Alexey Stakhov
Author: Bir Bahadur
Author: Harold Scott Macdonald Coxeter