Geometry And Its Applications In Arts Nature And Technology

This book returns geometry to its natural habitats: the arts, nature and technology. Throughout the book, geometry comes alive as a tool to unlock the understanding of our world. Assuming only familiarity with high school mathematics, the book invites the reader to discover geometry through examples from biology, astronomy, architecture, design, photography, drawing, engineering and more. Lavishly illustrated with over 1200 figures, all of the geometric results are carefully derived from scratch, with topics from differential, projective and non-Euclidean geometry, as well as kinematics, introduced as the need arises. The mathematical results contained in the book range from very basic facts to recent results, and mathematical proofs are included although not necessary for comprehension. With its wide range of geometric applications, this self-contained volume demonstrates the ubiquity of geometry in our world, and may serve as a source of inspiration for architects, artists, designers, engineers, and natural scientists. This new edition has been completely revised and updated, with new topics and many new illustrations.

Meyer's Geometry and Its Applications, Second Edition, combines traditional geometry with current ideas to present a modern approach that is grounded in real-world applications. It balances the deductive approach with discovery learning, and introduces axiomatic, Euclidean geometry, non-Euclidean geometry, and transformational geometry. The text integrates applications and examples throughout and includes historical notes in many chapters. The Second Edition of Geometry and Its Applications is a significant text for any college or university that focuses on geometry's usefulness in other disciplines. It is especially appropriate for engineering and science majors, as well as future mathematics teachers. Realistic applications integrated throughout the text, including (but not limited to): Symmetries of artistic patterns Physics Robotics Computer vision Computer graphics Stability of architectural structures Molecular biology Medicine Pattern recognition Historical notes included in many chapters

The purpose of this book is to analyze the interdisciplinary aspects of mathematics and geometry in reference to nature, art, and architecture.In Chapter 1, we introduce symmetry and its different meanings. Symmetry is a notion, which has been applied in the arts and architecture to find harmony and beauty. It joins aesthetics and practice, science and economy, mathematics and philosophy. In this chapter, we also analyze the influence of Vitruvius and the concept of old symmetry, received by the Renaissance. It is also interesting to note how in contemporary architecture there is often the presence of the "break" of symmetry (for example in the Frank O. Gehry's works).Chapter 2 explains how proportions, and in particular, the golden section, has introduced aesthetic canons that have strongly influenced many artists like Polycletus, and architects, from Ictinus to Le Corbusier.In Chapter 3, we discover how curves and spirals find their application in artistic works, for example in Mycenaean jewelry, and architectural works, from the Baroque of Francesco Borromini to the Land Art of Smithson.Chapter 4 presents the importance and influence that Platonic solids and polyhedrons have had on philosophy and art through different historical periods and different cultures. For instance, we look at how Platonic solids are connected to the theory of Empedocles' elements and Hippocrates' theory of humors.Chapter 5 describes surfaces, discovering how different cultures have used them in different manners, including Roman aqueducts, iron bridges, and finally arriving on modern structures that base their forms on hyperboloids and paraboloids.In Chapter 6, we introduce fractal geometry, as a geometry that tries to explain nature's irregular shapes, trying to overcome the limitations imposed by "old" Euclidean geometry. We also analyze how fractal geometry has influenced architecture in this century.

Geometrie, Physik und Biologie verstehen Das vorliegende Buch ist ein lehrreiches und reich bebildertes Sachbuch, das naturwissenschaftliche Inhalte auf anschauliche und verständliche Weise vermittelt. Anhand zahlreicher Beispiele erläutert es Themen aus Geometrie, Physik und Biologie und zeigt Gemeinsamkeiten zwischen den Disziplinen auf. Das Buch enthält rund 300 Links zu Videoanimationen; weiters steht eine frei zugängliche interaktive Software zur Verfügung, zur weiteren Vertiefung der Inhalte. Die Inhalte des Buches, die Videos und die Software wurden am Institut für Geometrie an der Universität für angewandte Kunst Wien entwickelt: Georg Glaeser forscht insbesondere zu interdisziplinären mathematischen und biologischen Fragestellungen und arbeitete viele Jahre gemeinsam mit Franz Gruber, einem Meister im Visualisieren komplexer Sachverhalte. Enthält Links zu rund 300 Videoanimationen, abrufbar über QR-Codes Kompakte, informative und leicht verständliche Erklärungen zu naturwissenschaftlichen Fragestellungen aus den Bereichen Geometrie, Physik und Biologie Mit zahlreichen Abbildungen und Illustrationen

This book will allow you to travel through time and space. To facilitate your journey, the editor has scoured the four corners of the earth in a quest for unusual people and their fascinating patterns. From Mozambique, to Asia, to many European countries, the contributors to The Pattern Book include world-famous cancer researchers, little-known artists and eclectirc computer programmers. Some of the patterns are ultramodern, while others are centuries old. Many of the patterns are drawn from the universe of mathematics. Computer recipes are scattered throughout.Although the emphasis is on computer-generated patterns, the book is informal and the intended audience spans several fields. The emphasis is on the fun that the true pattern lover finds in doing, rather than in reading about the doing! The book is organized into three main parts: Representing Nature (for those patterns which describe or show real physical phenomena, e.g., visualizations of protein motion, sea lilies, etc.), Mathematics and Symmetry (for those patterns which describe or show mathematical behavior, e.g. fractals), and Human Art (for those patterns which are artistic works of humans and made without the aid of a computer, e.g. Moslem tiling patterns.)

40 years of science visualization The visualization of often-encrypted data reveals new, previously hidden, but quite real worlds to humankind. Art adopts these insights and uses them to create new dimensions. This book brings together a wide range of contributions on visualization in science, media, and art. Renowned experts and associates of the Science Visualization Lab at the University of Applied Arts Vienna present examples of outstanding and innovative visualization projects and provide insight into their working methods. The book follows a variety of approaches to expanding perception and rendering the invisible visible. “If the doors of perception were cleansed, every thing would appear to man as it is, infinite.” – William Blake Insight into the thinking and working methods of renowned scientists, media experts, and artists Lavish publication with numerous illustrations and AR features With contributions by Ina Conradi / Mark Chavez, Christian Köberl, Walter Köhler, Thomas Matzek, Markus Müller, Ruth Schnell, Victoria Vesna / James K. Gimzewski, Manfred Wakolbinger, and others

In Pi (π) in Nature, Art, and Culture Marcel Danesi investigates the manifestations of π in science, nature, symbolism, and culture, arguing that these are intrinsically intertwined.

Mathematicians with special interest in biology, physics, geography, astronomy, architecture, design, etc., and being prepared to take pictures at any time, might try to answer unusual questions like the followings: What do a zebra, a tiger shark, and a hard coral have in common? How is this with drying mud, wings of dragon flies, and the structures of leaves? What is the “snail king” and is there also a “worm king”? Which curves stay of the same type after being photographed? Do fishes see like we do if we look through a fisheye lens? Which geometric properties of an object have physical consequences? Which kinds of geometric patterns appear when waves are interfering? In this book you can find 180 double pages with at least as many questions of this kind. The principle to attack a problem is often similar: It starts with a photo that is for some reasons remarkable. In a short description an explanation is offered, including relevant Internet links. Additionally one can frequently find computer simulations in order to illustrate and confirm.