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Author: Alekseĭ Vasilʹevich Shubnikov
Publisher: Springer
ISBN:
Category : Juvenile Nonfiction
Languages : en
Pages : 468
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Book Description
The perception of symmetry in art and in nature has been appreciated since antiquity, with development of the underlying laws tracing back at least to Pythagorean times. By the end of the eighteenth century it was realized that the immense variety of natural crystal shapes could be accounted for on the basis of a rather small number of symmetry operations, of which some were equally applicable to biological systems. The mathematical theory of symmetry continued to mature throughout the last century, culminating in the independent discoveries in Russia, Germany, and England that a total of only 230 independent ways exist in which the operations of rotation, reflection, and translation can be combined to transform three-dimensional geometrical objects into themselves. Derivation of the 230 space groups depends ultimately on restricting the meaning of symmetry to that of a property of purely geometrical figures. A. V. Shubnikov and his collaborators, over the past three decades, expanded this concept of symmetry to include the sign of transformation operations.
Author: Alekseĭ Vasilʹevich Shubnikov
Publisher: Springer
ISBN:
Category : Juvenile Nonfiction
Languages : en
Pages : 468
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Book Description
The perception of symmetry in art and in nature has been appreciated since antiquity, with development of the underlying laws tracing back at least to Pythagorean times. By the end of the eighteenth century it was realized that the immense variety of natural crystal shapes could be accounted for on the basis of a rather small number of symmetry operations, of which some were equally applicable to biological systems. The mathematical theory of symmetry continued to mature throughout the last century, culminating in the independent discoveries in Russia, Germany, and England that a total of only 230 independent ways exist in which the operations of rotation, reflection, and translation can be combined to transform three-dimensional geometrical objects into themselves. Derivation of the 230 space groups depends ultimately on restricting the meaning of symmetry to that of a property of purely geometrical figures. A. V. Shubnikov and his collaborators, over the past three decades, expanded this concept of symmetry to include the sign of transformation operations.
Author: Mark Allen
Publisher:
ISBN: 9780989956673
Category :
Languages : en
Pages :
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Book Description
Author: Katherine Larson
Publisher: Yale University Press
ISBN: 030017179X
Category : Poetry
Languages : en
Pages : 76
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Book Description
Katherine Larson is the winner of the 2010 Yale Series of Younger Poets Competition. With "Radial Symmetry," she has created a transcendent body of poems that flourish in the liminal spaces that separate scientific inquiry from empathic knowledge, astute observation from sublime witness. Larson's inventive lyrics lead the reader through vertiginous landscapes - geographical, phenomenological, psychological - while always remaining attendant to the speaker's own fragile, creaturely self. An experienced research scientist and field ecologist, Larson dazzles with these sensuous and sophisticated poems, grappling with the powers of poetic imagination as well as the frightful realization of the human capacity for ecological destruction. The result is a profoundly moving collection: eloquent in its lament and celebration. Metamorphosis [an excerpt]: We dredge the stream with soup strainers and separate dragonfly and damselfly nymphs - their eyes like inky bulbs, jaws snapping at the light as if the world was full of tiny traps, each hairpin mechanism tripped for transformation. Such a ricochet of appetites insisting life, life, life against the watery dark, the tuberous reeds.
Author: Werner Hahn
Publisher: World Scientific
ISBN: 9810223633
Category : Mathematics
Languages : en
Pages : 533
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Book Description
Looking beyond the boundaries of various disciplines, the author demonstrates that symmetry is a fascinating phenomenon which provides endless stimulation and challenges. He explains that it is possible to readapt art to the sciences, and vice versa, by means of an evolutionary concept of symmetry. Many pictorial examples are included to enable the reader to fully understand the issues discussed. Based on the artistic evidence that the author has collected, he proposes that the new ars evolutoria can function as an example for the sciences.The book is divided into three distinct parts, each one focusing on a special issue. In Part I, the phenomenon of symmetry, including its discovery and meaning is reviewed. The author looks closely at how Vitruvius, Polyclitus, Democritus, Plato, Aristotle, Plotinus, Augustine, Alberti, Leonardo da Vinci and Durer viewed symmetry. This is followed by an explanation on how the concept of symmetry developed. The author further discusses symmetry as it appears in art and science, as well as in the modern age. Later, he expounds the view of symmetry as an evolutionary concept which can lead to a new unity of science. In Part II, he covers the points of contact between the form-developing process in nature and art. He deals with biological questions, in particular evolution.The collection of new and precise data on perception and knowledge with regard to the postulated reality of symmetry leads to further development of the evolutionary theory of symmetry in Part III. The author traces the enormous treasure of observations made in nature and culture back to a few underlying structural principles. He demonstrates symmetry as a far-reaching, leading, structuring, causal element of evolution, as the idea lying behind nature and culture. Numerous controllable reproducible double-mirror experiments on a new stereoscopic vision verify a symmetrization theory of perception.
Author: Karyn Tripp
Publisher: Quarry Books
ISBN: 1631597701
Category : Juvenile Nonfiction
Languages : en
Pages : 115
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Book Description
In Math Art and Drawing Games for Kids, you’ll find an amazing collection of more than 40 hands-on art activities that make learning about math fun! Make Art + Learn Math Concepts = Become a Math Genius! Create fine art-inspired projects using math, including M. C. Escher’s tessellations, Wassily Kandinski’s abstractions, and Alexander Calder’s mobiles. Make pixel art using graph paper, grids, and dot grids. Explore projects that teach symmetry with mandala drawings, stained glass rose window art, and more. Use equations, counting, addition, and multiplication to create Fibonacci and golden rectangle art. Play with geometric shapes like spirals, hexagrams, and tetrahedrons. Learn about patterns and motifs used by cultures from all over the world, including Native American porcupine quill art, African Kente prints, and labyrinths from ancient Crete. Cook up some delicious math by making cookie tangrams, waffle fractions, and bread art. Take a creative path to mastering math with Math Art and Drawing Games for Kids!
Author: Frank A. Farris
Publisher: Princeton University Press
ISBN: 1400865670
Category : Art
Languages : en
Pages : 247
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Book Description
A step-by-step illustrated introduction to the astounding mathematics of symmetry This lavishly illustrated book provides a hands-on, step-by-step introduction to the intriguing mathematics of symmetry. Instead of breaking up patterns into blocks—a sort of potato-stamp method—Frank Farris offers a completely new waveform approach that enables you to create an endless variety of rosettes, friezes, and wallpaper patterns: dazzling art images where the beauty of nature meets the precision of mathematics. Featuring more than 100 stunning color illustrations and requiring only a modest background in math, Creating Symmetry begins by addressing the enigma of a simple curve, whose curious symmetry seems unexplained by its formula. Farris describes how complex numbers unlock the mystery, and how they lead to the next steps on an engaging path to constructing waveforms. He explains how to devise waveforms for each of the 17 possible wallpaper types, and then guides you through a host of other fascinating topics in symmetry, such as color-reversing patterns, three-color patterns, polyhedral symmetry, and hyperbolic symmetry. Along the way, Farris demonstrates how to marry waveforms with photographic images to construct beautiful symmetry patterns as he gradually familiarizes you with more advanced mathematics, including group theory, functional analysis, and partial differential equations. As you progress through the book, you'll learn how to create breathtaking art images of your own. Fun, accessible, and challenging, Creating Symmetry features numerous examples and exercises throughout, as well as engaging discussions of the history behind the mathematics presented in the book.
Author: Jay Kappraff
Publisher: World Scientific
ISBN: 9814491322
Category : Mathematics
Languages : en
Pages : 519
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Book Description
The first edition of Connections was chosen by the National Association of Publishers (USA) as the best book in “Mathematics, Chemistry, and Astronomy — Professional and Reference” in 1991. It has been a comprehensive reference in design science, bringing together in a single volume material from the areas of proportion in architecture and design, tilings and patterns, polyhedra, and symmetry. The book presents both theory and practice and has more than 750 illustrations. It is suitable for research in a variety of fields and as an aid to teaching a course in the mathematics of design. It has been influential in stimulating the burgeoning interest in the relationship between mathematics and design. In the second edition there are five new sections, supplementary, as well as a new preface describing the advances in design science since the publication of the first edition.
Author: György Darvas
Publisher: Springer Science & Business Media
ISBN: 3764375558
Category : Mathematics
Languages : en
Pages : 508
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Book Description
The first comprehensive book on the topic in half a century explores recent symmetry – and symmetry breaking – related discoveries, and discusses the questions and answers they raise in diverse disciplines: particle and high-energy physics, structural chemistry and the biochemistry of proteins, in genetic code study, in brain research, and also in architectural structures, and business decision making, to mention only a few examples.
Author: Bruno Gruber
Publisher: Springer Science & Business Media
ISBN: 140202634X
Category : Science
Languages : en
Pages : 623
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Book Description
This book is a collection of reviews and essays about the recent developments in the area of Symmetries and applications of Group Theory. Contributions have been written mostly at the graduate level but some are accessible to advanced undergraduates. The book is of interest to a wide audience and covers a broad range of topics with a strong degree of thematical unity. The book is part of a Series of books on Symmetries in Science and may be compared to the published Proceedings of the Colloquia on Group Theoretical Methods in Physics. Here, however, prevails a distinguished character for presenting extended reviews on present applications to Science, not restricted to Theoretical Physics.
Author: Tohru Ogawa
Publisher: Springer Science & Business Media
ISBN: 4431684077
Category : Science
Languages : en
Pages : 412
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Book Description
In Japanese culture the concept of katachi has special significance, connoting relationships and connectedness. Although katachi cannot be translated precisely, it corresponds most closely to "form," "shape," "pattern," or "Gestalt". The contemporary study of katachi is interdisciplinary and encompasses virtually all scientific and aesthetic endeavors. Katachi research seeks to bridge the gap between cultures - whether the "two cultures" of C.P. Snow or the contrasting cultures of East and West. To help achieve this aim and to foster international cooperation, the interdisciplinary symposium titled "Katachi "U" Symmetry" was convened in Tsukuba, Japan, November 21 - 25, 1994. With many participants from differing backgrounds and cultural perspectives, the symposium was the culmination of 15 years of work in the field. Like-minded researchers and philosophers came together from two movements in interdisciplinary studies of katachi and symmetry that arose in the 1980s, one in Japan, the other in Hungary. The proceedings of the symposium will stimulate and provoke the interest of scientists and mathematicians, engineers and architects, philosophers and semioticians - indeed, all those with a lively sense of curiosity and a wide-ranging intellect.
