The Geometrical Beauty of Plants

Author: Johan Gielis
Publisher: Springer
ISBN: 9789462391512
Release Date: 2017-06-01
Genre: Science

This book focuses on the origin of the Gielis curves, surfaces and transformations in the plant sciences. It is shown how these transformations, as a generalization of the Pythagorean Theorem, play an essential role in plant morphology and development. New insights show how plants can be understood as developing mathematical equations, which opens the possibility of directly solving analytically any boundary value problems (stress, diffusion, vibration...) . The book illustrates how form, development and evolution of plants unveil as a musical symphony. The reader will gain insight in how the methods are applicable in many divers scientific and technological fields.

The Algorithmic Beauty of Plants

Author: Przemyslaw Prusinkiewicz
Publisher: Springer Science & Business Media
ISBN: 9781461384762
Release Date: 2012-12-06
Genre: Computers

Now available in an affordable softcover edition, this classic in Springer's acclaimed Virtual Laboratory series is the first comprehensive account of the computer simulation of plant development. 150 illustrations, one third of them in colour, vividly demonstrate the spectacular results of the algorithms used to model plant shapes and developmental processes. The latest in computer-generated images allow us to look at plants growing, self-replicating, responding to external factors and even mutating, without becoming entangled in the underlying mathematical formulae involved. The authors place particular emphasis on Lindenmayer systems - a notion conceived by one of the authors, Aristid Lindenmayer, and internationally recognised for its exceptional elegance in modelling biological phenomena. Nonetheless, the two authors take great care to present a survey of alternative methods for plant modelling.


Author: Roger V. Jean
Publisher: Cambridge University Press
ISBN: 0521104696
Release Date: 2009-03-19
Genre: Mathematics

Phyllotaxis, the study of the patterns exhibited by leaves and other organs of plants, raises some of the deepest questions of plant morphogenesis. What principles of biological organisation produce these dynamical geometric systems? The constant occurrence of the Fibonacci sequence in such systems is a phenomenon that has fascinated botanists and mathematicians for centuries. In this book, first published in 1994, the many facets of phyllotaxis are dealt with in an integrated manner for the first time. The author describes a unified concept of phyllotaxis based on experimental, anatomical, cellular, physiological and paleontological observations. The book provides a framework for formal analyses of botanical data and emphasises the relevance of the phyllotactic paradigm in the study of other structures, such as crystals and proteins. It is of interest to cystallographers and physicists as well as to botanists and mathematicians.

The Hidden Geometry of Flowers

Author: Keith Critchlow
ISBN: 0863158064
Release Date: 2011
Genre: Mathematics

A beautiful and original book from a renowned thinker and geometrist

Sacred Geometry

Author: Stephen Skinner
Publisher: Sterling Publishing Company, Inc.
ISBN: 1402765827
Release Date: 2009
Genre: Mathematics

A fascinating and inspirational look at the vital link between the hidden geometrical order of the universe, geometry in nature, and the geometry of the man-made world. The Da Vinci Code has awakened the public to the powerful and very ancient idea that religious truths and mathematical principles are intimately intertwined. Sacred Geometry offers an accessible way of understanding how that connection is revealed in nature and the arts. Over the centuries, temple builders have relied on magic numbers to shape sacred spaces, astronomers have used geometry to calculate holy seasons, and philosophers have observed the harmony of the universe in the numerical properties of music. By showing how the discoveries of mathematics are manifested over and over again in biology and physics, and how they have inspired the greatest works of art, this illuminating study reveals the universal principles that link us to the infinite.

Principles of Dispersal in Higher Plants

Author: L. van der Pijl
Publisher: Springer Science & Business Media
ISBN: 9783662007990
Release Date: 2013-03-09
Genre: Science

The work offerred here is a companion volume to the work by K. FAEGRI and L. VAN DER PI]L "Principles of pollination ecology", which deals with the preceding phase of reproduction in plants. In the present work too, the emphasis is on principles and ecology. It is neither an enumeration of mechanisms, nor a compilation of cases. RIDLEY'S monumental work "The dispersal of plants throughout the world" already comprises 700 large pages of small print, and research has proceeded since then. Though this work is more than just 'a compilation and contains much insight and thoughts on principles in addition to reviews, its completeness hinders its use as a textbook. As a reference work, it is unsurpassed and the writer made frequent use of it. The writer paid special attention to functional backgrounds for the use of taxonomists working with "characters" and to biosystematics at the macro-level. He is indebted to Dr. P. MULLER-SCHNEIDER (Chur, Switzerland) for the permission to translate parts of his "Verbreitungsbiologie der Bliiten pflanzen" - of which permission a modest use has been made. Thanks are also due to 'the Director of the Rijksherbarium at Leyden, and to its librarian for the use of the library. Mr. F. J. NATAN was so kind as to make a number of photographs at the author's wishes.

Beautiful Geometry

Author: Eli Maor
Publisher: Princeton University Press
ISBN: 9781400848331
Release Date: 2014-01-19
Genre: Mathematics

If you've ever thought that mathematics and art don't mix, this stunning visual history of geometry will change your mind. As much a work of art as a book about mathematics, Beautiful Geometry presents more than sixty exquisite color plates illustrating a wide range of geometric patterns and theorems, accompanied by brief accounts of the fascinating history and people behind each. With artwork by Swiss artist Eugen Jost and text by math historian Eli Maor, this unique celebration of geometry covers numerous subjects, from straightedge-and-compass constructions to intriguing configurations involving infinity. The result is a delightful and informative illustrated tour through the 2,500-year-old history of one of the most important branches of mathematics.

Gems of Geometry

Author: John Barnes
Publisher: Springer Science & Business Media
ISBN: 9783642309649
Release Date: 2012-08-17
Genre: Mathematics

Based on a series of lectures for adult students, this lively and entertaining book proves that, far from being a dusty, dull subject, geometry is in fact full of beauty and fascination. The author's infectious enthusiasm is put to use in explaining many of the key concepts in the field, starting with the Golden Number and taking the reader on a geometrical journey via Shapes and Solids, through the Fourth Dimension, finishing up with Einstein's Theories of Relativity. Equally suitable as a gift for a youngster or as a nostalgic journey back into the world of mathematics for older readers, John Barnes' book is the perfect antidote for anyone whose maths lessons at school are a source of painful memories. Where once geometry was a source of confusion and frustration, Barnes brings enlightenment and entertainment. In this second edition, stimulated by recent lectures at Oxford, further material and extra illustrations have been added on many topics including Coloured Cubes, Chaos and Crystals.

Islamic Design

Author: Daud Sutton
Publisher: Wooden Books
ISBN: 9781912706037
Release Date: 2018-04-01
Genre: Art

Across the Islamic world, illuminating Korans from Morocco to Malaysia, and adorning mosques, mausoleums and palaces, are hidden some of the most exquisite geometrical devices ever conceived by man. In this excellent little book, geometer Daud Sutton unravels the mystery of Islamic patterns, explaining where they come from, how to draw them, and hinting at the Divine messages they encode. WOODEN BOOKS are small but packed with information. "Fascinating" FINANCIAL TIMES. "Beautiful" LONDON REVIEW OF BOOKS. "Rich and Artful" THE LANCET. "Genuinely mind-expanding" FORTEAN TIMES. "Excellent" NEW SCIENTIST. "Stunning" NEW YORK TIMES. Small books, big ideas.

Kiselev s Geometry

Author: Andreĭ Petrovich Kiselev
ISBN: UCSD:31822037285152
Release Date: 2008
Genre: Geometry

This volume completes the English adaptation of a classical Russian textbook in elementary Euclidean geometry. The 1st volume subtitled "Book I. Planimetry" was published in 2006 (ISBN 0977985202). This 2nd volume (Book II. Stereometry) covers solid geometry, and contains a chapter on vectors, foundations, and introduction in non-Euclidean geometry added by the translator. The book intended for high-school and college students, and their teachers. Includes 317 exercises, index, and bibliography.

Linguistic Geometry

Author: Boris Stilman
Publisher: Springer Science & Business Media
ISBN: 9781461544395
Release Date: 2012-12-06
Genre: Computers

Linguistic Geometry: From Search to Construction is the first book of its kind. Linguistic Geometry (LG) is an approach to the construction of mathematical models for large-scale multi-agent systems. A number of such systems, including air/space combat, robotic manufacturing, software re-engineering and Internet cyberwar, can be modeled as abstract board games. These are games with moves that can be represented by the movement of abstract pieces over locations on an abstract board. The purpose of LG is to provide strategies to guide the games' participants to their goals. Traditionally, discovering such strategies required searches in giant game trees. These searches are often beyond the capacity of modern and even conceivable future computers. LG dramatically reduces the size of the search trees, making the problems computationally tractable. LG provides a formalization and abstraction of search heuristics used by advanced experts including chess grandmasters. Essentially, these heuristics replace search with the construction of strategies. To formalize the heuristics, LG employs the theory of formal languages (i.e. formal linguistics), as well as certain geometric structures over an abstract board. The new formal strategies solve problems from different domains far beyond the areas envisioned by the experts. For a number of these domains, Linguistic Geometry yields optimal solutions.

Geometrical Vectors

Author: Gabriel Weinreich
Publisher: University of Chicago Press
ISBN: 0226890481
Release Date: 1998-07-06
Genre: Mathematics

Every advanced undergraduate and graduate student of physics must master the concepts of vectors and vector analysis. Yet most books cover this topic by merely repeating the introductory-level treatment based on a limited algebraic or analytic view of the subject. Geometrical Vectors introduces a more sophisticated approach, which not only brings together many loose ends of the traditional treatment, but also leads directly into the practical use of vectors in general curvilinear coordinates by carefully separating those relationships which are topologically invariant from those which are not. Based on the essentially geometric nature of the subject, this approach builds consistently on students' prior knowledge and geometrical intuition. Written in an informal and personal style, Geometrical Vectors provides a handy guide for any student of vector analysis. Clear, carefully constructed line drawings illustrate key points in the text, and problem sets as well as physical examples are provided.

A Beginner s Guide to Constructing the Universe

Author: Michael S. Schneider
Publisher: Harper Collins
ISBN: 9780062043160
Release Date: 2014-04-01
Genre: Science

The Universe May Be a Mystery, But It's No Secret Michael Schneider leads us on a spectacular, lavishly illustrated journey along the numbers one through ten to explore the mathematical principles made visible in flowers, shells, crystals, plants, and the human body, expressed in the symbolic language of folk sayings and fairy tales, myth and religion, art and architecture. This is a new view of mathematics, not the one we learned at school but a comprehensive guide to the patterns that recur through the universe and underlie human affairs. A Beginner's Guide to Constructing, the Universe shows you: Why cans, pizza, and manhole covers are round. Why one and two weren't considered numbers by the ancient Greeks. Why squares show up so often in goddess art and board games. What property makes the spiral the most widespread shape in nature, from embryos and hair curls to hurricanes and galaxies. How the human body shares the design of a bean plant and the solar system. How a snowflake is like Stonehenge, and a beehive like a calendar. How our ten fingers hold the secrets of both a lobster and a cathedral. And much more.

The Computational Beauty of Nature

Author: Gary William Flake
Publisher: MIT Press
ISBN: 0262561271
Release Date: 1998
Genre: Computers

Gary William Flake develops in depth the simple idea that recurrent rules can produce rich and complicated behaviors.