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.
In this book, topics such as algebra, trigonometry, calculus and statistics are brought to life through over 500 applications ranging from biology, physics and chemistry to astronomy, geography and music. With over 600 illustrations emphasizing the beauty of mathematics, Math Tools complements more theoretical textbooks on the market, bringing the subject closer to the reader and providing a useful reference to students. By highlighting the ubiquity of mathematics in practical fields, the book will appeal not only to students and teachers, but to anyone with a keen interest in mathematics and its applications.
With fascinating, spectacularly beautiful images, the book piques readers’ curiosity about the diversity of visual organs. This book is the result of a dual approach – scientific as well as aesthetic. The compelling images are accompanied by an easy-to-read, understandable text, aimed at both scientists and the educated public, and generally anyone interested in the beauty of nature. Thanks to this combination, the book presents the staggering diversity of eyes in the animal kingdom and provides countless insights into the intriguing mechanisms at work – from simple pigment cups to independently flexible, telescopic, facet and lens eyes. Educational, exciting, entertaining till the last page, this is a book for anyone who is interested in evolution, nature and the miracle of life.
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.
Understanding geometry, physics, and biology This is a highly informative and richly illustrated nonfiction book that conveys scientific content in a clear and understandable way. Drawing on numerous examples, it explains topics from geometry, physics, and biology and points out commonalities between the disciplines. The book contains approx. 300 links to video animations and is accompanied by a freely accessible interactive software that allows readers to delve even deeper into the content covered in the book. The content, videos, and software were developed by the Department of Geometry at the University of Applied Arts Vienna. Georg Glaeser’s research focuses particularly on interdisciplinary mathematical and biological issues, and he worked for many years with Franz Gruber, who was highly adept at visualizing complex issues. Includes links to around 300 video animations, accessible via QR codes Compact, informative, and easy-to-understand explanations of scientific issues in the disciplines of geometry, physics, and biology With numerous images and illustrations
This text presents the classical theory of conics in a modern form. It includes many novel results that are not easily accessible elsewhere. The approach combines synthetic and analytic methods to derive projective, affine and metrical properties, covering both Euclidean and non-Euclidean geometries. With more than two thousand years of history, conic sections play a fundamental role in numerous fields of mathematics and physics, with applications to mechanical engineering, architecture, astronomy, design and computer graphics. This text will be invaluable to undergraduate mathematics students, those in adjacent fields of study, and anyone with an interest in classical geometry. Augmented with more than three hundred fifty figures and photographs, this innovative text will enhance your understanding of projective geometry, linear algebra, mechanics, and differential geometry, with careful exposition and many illustrative exercises.
The Universe of Quadrics This text presents the theory of quadrics in a modern form. It builds on the previously published book "The Universe of Conics", including many novel results that are not easily accessible elsewhere. As in the conics book, the approach combines synthetic and analytic methods to derive projective, affine, and metrical properties, covering both Euclidean and non-Euclidean geometries. While the history of conics is more than two thousand years old, the theory of quadrics began to develop approximately three hundred years ago. Quadrics play a fundamental role in numerous fields of mathematics and physics, their applications ranging from mechanical engineering, architecture, astronomy, and design to computer graphics. This text will be invaluable to undergraduate and graduate mathematics students, those in adjacent fields of study, and anyone with a deeper interest in geometry. Complemented with about three hundred fifty figures and photographs, this innovative text will enhance your understanding of projective geometry, linear algebra, mechanics, and differential geometry, with careful exposition and many illustrative exercises.
This book will take you on an exciting journey made up of texts and images. Spectacular, large-scale photographs printed on double pages and accompanied by explanatory texts will arouse the reader’s curiosity about evolution’s accomplishments in the world of flying: from the botanical air fleet (pollen grains, flying seeds...), over flying snakes and fish, to penguins flying underwater and humans rising into the air. Mathematician and passionate animal photographer Georg Glaser has joined forces with the experienced evolutionary biologist Hannes Paulus and the exercise physiologist and flight biophysicist Werner Nachtigall in order to approach this topic with words and pictures in a way that is both generally comprehensible and scientifically sound. Double-page by double-page, the book can be read in any order. Cross-references allow to jump easily from one double-page to another. Aside from the detailed introduction to each chapter, the text passages are usually independent from one another, and they discuss crucial moments in the evolutionary process. The double-pages provide additional information on bibliographical references and references to informative websites.
The artist Markus Roskar and Professor of Mathematics, Georg Glaeser, (who both teach at the University for Applied Arts in Vienna) have written a mathematics book of the other kind. In this book, mathematics sheds its image as an inaccessible, cumbersome science, and acquires an open and emotional dimension. The book is structured on the double-page principle: each double page includes an almost always humorous professional drawing that relates to the text on the other page. This text is written in an easy-going, often humorous, but always mathematically correct manner. It mostly deals with an everyday subject that has a mathematical background or an unorthodox mathematical question. Readers can count on a wealth of surprising solutions to often complex problems.
The Moon has always been an object of immense fascination for humanity – and not just because of its prominence in the night sky. With its complex orbit, it is far closer to our planet than any other celestial body. Already in ancient Babylon, humans have studied the Moon and its relationship to the planets and constellations. Through incisive texts and illustrations using photos and computer simulations, this book explores the similarities and differences to other planets and their moons, the Moon’s interactions with the Sun and the Earth, and interesting historical associations. In addition to scientifically accurate texts, it contains numerous large-format photographs and graphics that vividly explain the complex phenomenon of the Moon. Richly illustrated, it is designed for anyone interested in astronomy.
With spectacular large-format images complemented by scientifically grounded, yet easy-to-read, explanatory texts, Georg Glaeser and Werner Nachtigall take you on an exciting journey through the fascinating world of macrostructures – small structures in nature that fulfill specific functions. This book will pique your curiosity about a secret world known only to a few by presenting an impressive range of evolutionary mechanisms, from shrimps’ “tail flips” to the adhesive pads of gecko setae and the implementation of biological structures in the field of bionics. The book can be read in any fashion you please – the cross-references make it easy to jump across the sections, which are largely self-contained and discuss various highlights of the evolutionary process.
At once a programming course that emphasises object-oriented thinking as well as a well-documented, versatile, and robust geometry library. All of the relevant geometry is covered in depth to provide a good understanding of the background to this topic. Many of the most common intersection problems and measuring tasks are covered, with the authors discussing the creation of arbitrary geometric objects and the use of Boolean operations to create more general solid objects. As a result, all those looking for an in-depth introduction to graphics programming will find this a solid, hands-on text.
In this book, a variety of algoritbms are described that may be of interest to everyone who writes software for 3D-graphics. It is a book that haB been written for programmers at an intermediate level as well aB for experienced software engineers who simply want to have some particular functions at their disposal, without having to think too much about details like special cases or optimization for speed. The programming language we use is C, and that has many advantages, because it makes the code both portable and efficient. Nevertheless, it should be possible to adapt the ideas to other high-level programming languages. The reader should have a reasonable knowledge of C, because sophisticated pro grams with economical storage household and fast sections cannot be written without the use of pointers. You will find that in the long run it is just aB easy to work with pointer variables as with multiple arrays . .Aß the title of the book implies, we will not deal with algorithms that are very computation-intensive such as ray tracing or the radiosity method. Furthermore, objects will always be (closed or not closed) polyhedra, which consist of a certain number of polygons.
This Handbook fills the gaps of Open Geometry by explaining new methods, techniques and various examples. One its main strengths is that it enables the reader to learn about Open Geometry by working through examples. In addition, it includes a complete compendium of all the Open Geometry classes and their methods. Open Geometry will be of great attraction to those who want to start graphics programming.
This book invites snorkelers and divers on an educational visit to the most important ecosystems of the Mediterranean Sea. Keystone species from brown algae to dolphins are presented in their marine habitats and understood as part of a complex ecological system. Instead of grouping animals and plants taxonomically, we have organised them according to the eight main habitats of the Mediterranean Sea. Our journey starts with different types of rocky grounds, then takes you further to the Mediterranean’s sandy and muddy grounds, and finally ends with the fish and dolphins of the blue open sea. You will be introduced to 220 ecologically significant animal and plant species via the texts of Daniel Abed-Navandi, a long-time lecturer on the biodiversity of the Mediterranean Sea at the University of Vienna, and the photographs of Georg Glaeser, the master behind the camera, who captures marine life on the spot.
How can one visualize a curve that fills the entire plane or all of space? Can a polyhedron be smoothly turned inside out? What is the projective plane? What does four-dimensional space look like? Can soap bubbles exist that are not spherical? How can one better understand the structure of vortices and currents? In this book you will experience mathematics from the visual point of view, discovering fascinating and never previously published images that offer illustrative examples to the above questions. Every picture is accompanied by a brief explanatory text, references to further reading, and a number of web links where you can obtain further information. This book is intended for all friends of mathematics—students, teachers, amateurs, and professionals—who want to see something beyond dry text and endless formulas. It will provide inspiration for pursuing further one or another topic that may previously have seemed inaccessible. You will get to know mathematics from a totally new and colorful viewpoint.
Illustrating the use of C, with stress on portability and speed, this book provides a mathematical background to techniques in computer graphics, before going on to develop a graphics program in C implementing these techniques. As a result, both students and professionals will find this presentation gives them a thorough understanding of the most fundamental algorithms in graphics programming, as well as providing them with a usable graphics package. Georg Glaeser covers such hot topics as hidden surfaces, shadows, reflections, patterns, and modelling curves and surfaces. Readers are assumed to be moderately familiar with programming, although all type definitions, global variables, and macros are thoroughly described prior to their first applications.
At once a programming course that emphasises object-oriented thinking as well as a well-documented, versatile, and robust geometry library. All of the relevant geometry is covered in depth to provide a good understanding of the background to this topic. Many of the most common intersection problems and measuring tasks are covered, with the authors discussing the creation of arbitrary geometric objects and the use of Boolean operations to create more general solid objects. As a result, all those looking for an in-depth introduction to graphics programming will find this a solid, hands-on text.
With fascinating, spectacularly beautiful images, the book piques readers’ curiosity about the diversity of visual organs. This book is the result of a dual approach – scientific as well as aesthetic. The compelling images are accompanied by an easy-to-read, understandable text, aimed at both scientists and the educated public, and generally anyone interested in the beauty of nature. Thanks to this combination, the book presents the staggering diversity of eyes in the animal kingdom and provides countless insights into the intriguing mechanisms at work – from simple pigment cups to independently flexible, telescopic, facet and lens eyes. Educational, exciting, entertaining till the last page, this is a book for anyone who is interested in evolution, nature and the miracle of life.
Understanding geometry, physics, and biology This is a highly informative and richly illustrated nonfiction book that conveys scientific content in a clear and understandable way. Drawing on numerous examples, it explains topics from geometry, physics, and biology and points out commonalities between the disciplines. The book contains approx. 300 links to video animations and is accompanied by a freely accessible interactive software that allows readers to delve even deeper into the content covered in the book. The content, videos, and software were developed by the Department of Geometry at the University of Applied Arts Vienna. Georg Glaeser’s research focuses particularly on interdisciplinary mathematical and biological issues, and he worked for many years with Franz Gruber, who was highly adept at visualizing complex issues. Includes links to around 300 video animations, accessible via QR codes Compact, informative, and easy-to-understand explanations of scientific issues in the disciplines of geometry, physics, and biology With numerous images and illustrations
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.
Many people have great ideas. Without the necessary skills and means most never get to realize them. If they could cooperate with competent firms and entrepreneurs together both could achieve much and this is increasingly happening. Mechanisms are being established making a division of labour between inventors and implementers a reality. This is changing the nature of innovation from an internal R&D, or purely entrepreneurial attempt, to a more cooperative innovation. An Idea Economy emerges, where anyone has the possibility to profit from their ideas, and everyone will benefit from more and better innovation. This book presents us the emergence and structure of the Idea Economy by extending the seminal concepts of Entrepreneurial Society and Open Innovation. Part I describes the big picture on how innovation is evolving, where we are today, and what an Idea Economy will look like. Part II points the way forward, discussing in detail on how cooperation in the innovation process works, and why this is only recently becoming possible.
The glasshouses of the nineteenth century represent a remarkable confluence of opposites in architecture and technology. The architecture was designed to create an artificial climate in which people could return to paradise, and yet the technical means employed were also basic to the century's developing industrial grime -the other side of paradise. Enriched by more than 700 illustrations, Houses of Glass chronicles these pristine structures as they evolved from hothouses into exhibition halls, ballrooms, and theaters. Georg Kohlmaier is an architect and Barna von Sartory a sculptor. They have collaborated on many books and articles on contemporary architecture.
This book compiles the papers and comments delivered at the Confârence on "European and American constitutionaism" which took place in Gèttingen in 2003. Through topics like freedom of speech, human dignity, the protective function of the state, adjudication and democracy and international influences, the conference papers identify salient features of the constitutional systems on both sides of the Atlantic and address recent developments following the end of the soviet era in eastern Europe and the terrorists attacks of 11 September 2001.
An autobiographical novel of World War I experiences in the German ranks, Zero Hour equates duty with camaraderie and finds a balance between bitterness and hawkishness. The war is experienced here through the keen eyes of Hans Volkenborn, a well-bred officer-candidate whose youthful enthusiasm turns to angst and disillusion. The sole comfort of his experience is fellowship with his comrades, but even that abates over time.
This open access textbook provides a concise introduction to economic approaches and mathematical methods for the study of water allocation and distribution problems. Written in an accessible and straightforward style, it discusses and analyzes central issues in integrated water resource management, water tariffs, water markets, and transboundary water management. By illustrating the interplay between the hydrological cycle and the rules and institutions that govern today’s water allocation policies, the authors develop a modern perspective on water management. Moreover, the book presents an in-depth assessment of the political and ethical dimensions of water management and its institutional embeddedness, by discussing distribution issues and issues of the enforceability of human rights in managing water resources. Given its scope, the book will appeal to advanced undergraduate and graduate students of economics and engineering, as well as practitioners in the water sector, seeking a deeper understanding of economic approaches to the study of water management.
This is the long-awaited third edition of this highly regarded comparative overview of corporate law. This edition has been comprehensively revised and updated to reflect the profound changes in corporate law and governance practices that have taken place since the previous edition. These include numerous regulatory changes following the financial crisis of 2007-09 and the changing landscape of governance, especially in the US, with the ever more central role of institutional investors as (active) owners of corporations. The geographic scope of the coverage has been broadened to include an important emerging economy, Brazil. In addition, the book now incorporates analysis of the burgeoning use of corporate law to protect the interests of "external constituencies" without any contractual relationship to a company, in an attempt to tackle broader social and economic problems. The authors start from the premise that corporations (or companies) in all jurisdictions share the same key legal attributes: legal personality, limited liability, delegated management, transferable shares, and investor ownership. Businesses using the corporate form give rise to three basic types of agency problems: those between managers and shareholders as a class; controlling shareholders and minority shareholders; and shareholders as a class and other corporate constituencies, such as corporate creditors and employees. After identifying the common set of legal strategies used to address these agency problems and discussing their interaction with enforcement institutions, The Anatomy of Corporate Law illustrates how a number of core jurisdictions around the world deploy such strategies. In so doing, the book highlights the many commonalities across jurisdictions and reflects on the reasons why they may differ on specific issues. The analysis covers the basic governance structure of the corporation, including the powers of the board of directors and the shareholder meeting, both when management and when a dominant shareholder is in control. It then analyses the role of corporate law in shaping labor relationships, protection of external stakeholders, relationships with creditors, related-party transactions, fundamental corporate actions such as mergers and charter amendments, takeovers, and the regulation of capital markets. The Anatomy of Corporate Law has established itself as the leading book in the field of comparative corporate law. Across the world, students and scholars at various stages in their careers, from undergraduate law students to well-established authorities in the field, routinely consult this book as a starting point for their inquiries.
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