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.

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.

The Geometry of Fractal Sets

Author: K. J. Falconer
Publisher: Cambridge University Press
ISBN: 0521337054
Release Date: 1986-07-24
Genre: Mathematics

This book contains a rigorous mathematical treatment of the geometrical aspects of sets of both integral and fractional Hausdorff dimension. Questions of local density and the existence of tangents of such sets are studied, as well as the dimensional properties of their projections in various directions. In the case of sets of integral dimension the dramatic differences between regular 'curve-like' sets and irregular 'dust like' sets are exhibited. The theory is related by duality to Kayeka sets (sets of zero area containing lines in every direction). The final chapter includes diverse examples of sets to which the general theory is applicable: discussions of curves of fractional dimension, self-similar sets, strange attractors, and examples from number theory, convexity and so on. There is an emphasis on the basic tools of the subject such as the Vitali covering lemma, net measures and Fourier transform methods.

Geometry A Comprehensive Course

Author: Dan Pedoe
Publisher: Courier Corporation
ISBN: 9780486131733
Release Date: 2013-04-02
Genre: Mathematics

Introduction to vector algebra in the plane; circles and coaxial systems; mappings of the Euclidean plane; similitudes, isometries, Moebius transformations, much more. Includes over 500 exercises.

Phyllotaxis

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.

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.

The Hidden Geometry of Flowers

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

A beautiful and original book from a renowned thinker and geometrist

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.

Computational Geometry

Author: Mark de Berg
Publisher: Springer Science & Business Media
ISBN: 9783540779735
Release Date: 2008-03-07
Genre: Computers

This introduction to computational geometry focuses on algorithms. Motivation is provided from the application areas as all techniques are related to particular applications in robotics, graphics, CAD/CAM, and geographic information systems. Modern insights in computational geometry are used to provide solutions that are both efficient and easy to understand and implement.

Drawing Geometry

Author:
Publisher:
ISBN: 0863156088
Release Date: 2007
Genre: Architecture

A professional guide to drawing two-dimensional geometric shapes in simple step-by-step instructions.

Advanced Euclidean Geometry

Author: Roger A. Johnson
Publisher: Courier Corporation
ISBN: 9780486154985
Release Date: 2013-01-08
Genre: Mathematics

This classic text explores the geometry of the triangle and the circle, concentrating on extensions of Euclidean theory, and examining in detail many relatively recent theorems. 1929 edition.

College Geometry

Author: Nathan Altshiller-Court
Publisher: Courier Corporation
ISBN: 9780486141374
Release Date: 2012-06-29
Genre: Mathematics

The standard university-level text for decades, this volume offers exercises in construction problems, harmonic division, circle and triangle geometry, and other areas. 1952 edition, revised and enlarged by the author.

Lines and Curves

Author: Victor Gutenmacher
Publisher: Springer Science & Business Media
ISBN: 9781475738094
Release Date: 2013-03-14
Genre: Mathematics

Broad appeal to undergraduate teachers, students, and engineers; Concise descriptions of properties of basic planar curves from different perspectives; useful handbook for software engineers; A special chapter---"Geometry on the Web"---will further enhance the usefulness of this book as an informal tutorial resource.; Good mathematical notation, descriptions of properties of lines and curves, and the illustration of geometric concepts facilitate the design of computer graphics tools and computer animation.; Video game designers, for example, will find a clear discussion and illustration of hard-to-understand trajectory design concepts.; Good supplementary text for geometry courses at the undergraduate and advanced high school levels