This concise review examines the geometry of the straight line, circle, plane, and sphere as well as their associated configurations, including the triangle and the cylinder. Aimed at university undergraduates, the treatment is also useful for advanced students at the secondary level. The straightforward approach begins with a recapitulation of previous work on the subject, proceeding to explorations of advanced plane geometry, solid geometry with some reference to the geometry of the sphere, and a chapter on the nature of space, including considerations of such properties as congruence, similarity, and symmetry. The text concludes with a brief account of the elementary transformations of projection and inversion. Numerous examples appear throughout the book.
In this book, first-time author Abhishek Mukherjee provides us with a fresh take on romance and relationships. The book unfolds as the protagonist tries to break free from her mediocre life and is ready to trade her life for a deal on her dreams. But she soon finds out that everything is not as it looks like when she starts living with her rescuer and discovers the mighty walls of the mansion whispering secrets about her rescuer’s political family. Friendships are made along the way as she starts trusting those around her. But how long will her trust sustain!The Fall before the Rise is a fast-paced novel that will keep its grip on your attention as the protagonist takes you through her journey in her own words as she discovers relationships budding in the most barren of situations. A story of love and blood, hate and white lies, dreams and reality, it surprises you when you least expect it. Full of unexpected twist, it provides for an exhilarating read.
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
This book is a collection of surveys and exploratory articles about recent developments in the field of computational Euclidean geometry. The topics covered are: a history of Euclidean geometry, Voronoi diagrams, randomized geometric algorithms, computational algebra; triangulations, machine proofs, topological designs, finite-element mesh, computer-aided geometric designs and steiner trees. Each chapter is written by a leading expert in the field and together they provide a clear and authoritative picture of what computational Euclidean geometry is and the direction in which research is going.
This book is a collection of surveys and exploratory articles about recent developments in the field of computational Euclidean geometry. Topics covered include the history of Euclidean geometry, Voronoi diagrams, randomized geometric algorithms, computational algebra, triangulations, machine proofs, topological designs, finite-element mesh, computer-aided geometric designs and Steiner trees. This second edition contains three new surveys covering geometric constraint solving, computational geometry and the exact computation paradigm.
In recent years geometry seems to have lost large parts of its former central position in mathematics teaching in most countries. However, new trends have begun to counteract this tendency. There is an increasing awareness that geometry plays a key role in mathematics and learning mathematics. Although geometry has been eclipsed in the mathematics curriculum, research in geometry has blossomed as new ideas have arisen from inside mathematics and other disciplines, including computer science. Due to reassessment of the role of geometry, mathematics educators and mathematicians face new challenges. In the present ICMI study, the whole spectrum of teaching and learning of geometry is analysed. Experts from all over the world took part in this study, which was conducted on the basis of recent international research, case studies, and reports on actual school practice. This book will be of particular interest to mathematics educators and mathematicians who are involved in the teaching of geometry at all educational levels, as well as to researchers in mathematics education.
This book re-examines the nature of early Chinese work in natural science, on the basis of original records analysis and artifacts discovered in recent decades by archaeological explorations of China's past. It presents a concise account of early scientific ideas and thoughts of nature, and their effect on the development of natural science. It is suggested that the traditional characterization of early Chinese work in natural science requires substantial modification. The absence of early Chinese participation in the development of 'modern' science is not, as commonly assumed, a consequence of lacking early scientific tradition in ancient China. It is argued that the concept of 'inhibitive' factors is dubious without taking their dynamical relationships into account, and that socio-economical and political influence has to be considered when seeking answers to the major setbacks in science and technology in China. The book also shows that there is no basis for the claims saying that acoustics and astronomy in China have their roots in Babylon.
Among the many conceits of modern thought is the idea that philosophy, tainted as it is by subjective evaluation, is a shaky guide for human affairs. People, it is argued, are better off if they base their conduct either on know-how with its pragmatic criterion of truth (i.e., possibility) or on science with its universal criterion of rational necessity. Since Helmholtz, there has been increasing concern in the life sciences about the role of reductionism in the construction of knowledge. Is psychophysics really possible? Are biological phenomena just the deducible results of chemical phenomena? And if life can be reduced to molecular mechanisms only, where do these miraculous molecules come from, and how do they work? On a psychological level, people wonder whether psychological phenomena result simply from genetically hardwired structures in the brain or whether, even if not genetically determined, they can be identified with the biochemical processes of that organ. In sociology, identical questions arise. If physical or chemical reduction is not practicable, should we think in terms of other forms of reduction, say, the reduction of psychological to sociological phenomena or in terms of what Piaget has called the "reduction of the lower to the higher" (e.g., teleology)? All in all, then, reductionism in both naive and sophisticated forms permeates all of human thought and may, at least in certain cases, be necessary to it. If so, what exactly are those cases? The papers collected in this volume are all derived from the 29th Annual Symposium of the Jean Piaget Society. The intent of the volume is to examine the issue of reductionism on the theoretical level in several sciences, including biology, psychology, and sociology. A complementary intent is to examine it from the point of view of the practical effects of reductionistic doctrine on daily life.
