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Two classic tales of near-future politics and skulduggery are twice the bargain in this newest Tor Double. Superior reading by award-winning authors.

This Student Lab Manual is to accompany Symmetry, Shape, and Space, which uses the visual nature of geometry to involve readers in discovering mathematics. The text allows readers to study and analyze patterns for themselves, which in turn teaches creativity, as well as analytical and visualization skills. Varied content, activities, and examples lead readers into an investigative process and provide the experience of doing and discovering mathematics as mathematicians do. Exercises requiring readers to express their ideas in writing and to create drawings or physical models make math a hands-on experience. Assuming no mathematics beyond the high school level, Symmetry, Shape, and Space is the perfect introduction to mathematics, and it is designed so that each chapter is independent of the others, allowing great flexibility.

Buried beneath today's Midwestern towns, under several layers of earth and the accumulated debris of two thousand years, are the clues to an ancient mystery. A Native American people, now known as the Hopewell, lived and worked these lands, building earthworks which in some instances dwarf the ruins at Stonehenge. More significantly, these mammoth earthworks were built in different geometric shapes, using a standard unit of measure and aligned to the cycles of the sun and the moon. Using the foundation of existing scholarship, Mysteries of the Hopewell presents new discoveries showing the accomplishments of the Mound Builders in astronomy, geometry, measurement, and counting. William Romain then goes one step further to theorize why generations of people toiled to move millions of tons of earth to form these precise structures, joining the ranks of the Egyptians, Mayans, Greeks, Chinese, and other advanced ancient cultures. William Romain's Mysteries of the Hopewell will appeal to many readers, including anthropologists, mathematicians, and historians, but perhaps especially to readers curious about ancient cultures and seeking explanations for these magnificent earthen structures.

No dust jacket. Good hardcover with some shelfwear; may have previous owner's name inside. Standard-sized.

Buried beneath today's Midwestern towns, under several layers of earth and the accumulated debris of two thousand years, are the clues to an ancient mystery. A Native American people, now known as the Hopewell, lived and worked these lands, building earthworks which in some instances dwarf the ruins at Stonehenge. More significantly, these mammoth earthworks were built in different geometric shapes, using a standard unit of measure and aligned to the cycles of the sun and the moon. Using the foundation of existing scholarship, Mysteries of the Hopewell presents new discoveries showing the accomplishments of the Mound Builders in astronomy, geometry, measurement, and counting. William Romain then goes one step further to theorize why generations of people toiled to move millions of tons of earth to form these precise structures, joining the ranks of the Egyptians, Mayans, Greeks, Chinese, and other advanced ancient cultures. William Romain's Mysteries of the Hopewell will appeal to many readers, including anthropologists, mathematicians, and historians, but perhaps especially to readers curious about ancient cultures and seeking explanations for these magnificent earthen structures.

Deals with the life and work of the great twentieth-century mathematician Shiing-Shen Chern. Included are numerous pages of photographs; an autobiographical article recounting the formation of a mathematical mind and of a great war; historical and personal reminiscences by thirty distinguished mathematicians and physicists including Bott, Griffiths, Lawson, Nirenberg, Singer, Yang, Yau, and others; and a discussion of 100 open problems in geometry. The book is essential for anyone who is interested in understanding Chern and his influence upon twentieth-century century mathematics.

Buried beneath today's Midwestern towns, under several layers of earth and the accumulated debris of two thousand years, are the clues to an ancient mystery. A Native American people, now known as the Hopewell, lived and worked these lands, building earthworks which in some instances dwarf the ruins at Stonehenge. More significantly, these mammoth earthworks were built in different geometric shapes, using a standard unit of measure and aligned to the cycles of the sun and the moon. Using the foundation of existing scholarship, Mysteries of the Hopewell presents new discoveries showing the accomplishments of the Mound Builders in astronomy, geometry, measurement, and counting. William Romain then goes one step further to theorize why generations of people toiled to move millions of tons of earth to form these precise structures, joining the ranks of the Egyptians, Mayans, Greeks, Chinese, and other advanced ancient cultures. William Romain's Mysteries of the Hopewell will appeal to many readers, including anthropologists, mathematicians, and historians, but perhaps especially to readers curious about ancient cultures and seeking explanations for these magnificent earthen structures.

College Geometry Using The Geometer's Sketchpad(R) is unique in its truly discovery based approach to learning geometry with complete integration of Sketchpad. Through explorations of topics ranging from triangles and circles to transformational, taxicab, and hyperbolic geometries, students hone their understanding of geometry and their ability to write rigorous mathematical proofs. It is an ideal text for students planning to teach at the middle or secondary level. Each chapter follows the same format to best promote active learning: - Activities open each chapter allowing students the opportunity to explore topics and make conjectures using Sketchpad - Discussions cover important theorems and concepts that solidify the conjectures made in the activities - Exercises reinforce the discussions and advance student expertise with Sketchpad - Each new copy of the book is packaged with a valuable CD-ROM with Sketchpad documents that relate directly to the material in the text - These multi-page documents provide a starting point for every activity and provide dynamic interactive versions of all the figures in the text.

Starting with an analysis of the forms of symmetry, the authors show how a few key principles can help us understand everything from cat's movements, corn circles, and snow crystals to subatomic particles and the overall structure of the cosmos. 127 figures. of full-color illustrations.

Felix Klein, a great geometer of the nineteenth century, rediscovered an idea from Hindu mythology in mathematics: the heaven of Indra in which the whole Universe was mirrored in each pearl in a net of pearls. Practically impossible to represent by hand, this idea barely existed outside the imagination, until the 1980s when the authors embarked on the first computer investigation of Klein's vision. In this extraordinary book they explore the path from some basic mathematical ideas to the simple algorithms that create delicate fractal filigrees, most appearing in print for the first time. Step-by-step instructions for writing computer programs allow beginners to generate the images.

Hobbes's philosophical discourse is deconstructed as the interplay of the drama of individual behaviour as perceived by rational agents and the detached analysis of conflict by a political geometer . The author solves some long-standing problems in Hobbesian political philosophy (e.g., the role of glory, Hobbes' pessimism) and shows the consistency of Hobbes' attempt to derive absolutism as the only stable political association. Although based on extensive textual analysis of Hobbes' works and correspondence, the book is an exercise in political philosophy that students will find iconoclastic and experts challenging.

This lavishly illustrated book provides an unusually accessible approach to geometry by placing it in historical context. With concise discussions and carefully chosen illustrations the author brings the material to life by showing what problems motivated early geometers throughout the world. Geometry Civilized covers classical plane geometry, emphasizing the methods of Euclid but also drawing on advances made in China and India. It includes a wide range of problems, solutions, and illustrations, as well as a chapter on trigonometry, and prepares its readers for the study of solid geometry and conic sections.

The complete works of antiquity's great geometer appear here in a highly accessible English translation by a distinguished scholar. Remarkable for his range of thought and his mastery of treatment, Archimedes addressed such topics as the famous problems of the ratio of the areas of a cylinder and an inscribed sphere; the measurement of a circle; the properties of conoids, spheroids, and spirals; and the quadrature of the parabola. This edition offers an informative introduction with many valuable insights into the ancient mathematician's life and thought as well as the views of his contemporaries. Modern mathematicians, physicists, science historians, and logicians will find this volume a source of timeless fascination. Unabridged, with supplement.

Rational points on algebraic curves over finite fields is a key topic for algebraic geometers and coding theorists. Here, the authors relate an important application of such curves, namely, to the construction of low-discrepancy sequences, needed for numerical methods in diverse areas. They sum up the theoretical work on algebraic curves over finite fields with many rational points and discuss the applications of such curves to algebraic coding theory and the construction of low-discrepancy sequences.

Rational points on algebraic curves over finite fields is a key topic for algebraic geometers and coding theorists. Here, the authors relate an important application of such curves, namely, to the construction of low-discrepancy sequences, needed for numerical methods in diverse areas. They sum up the theoretical work on algebraic curves over finite fields with many rational points and discuss the applications of such curves to algebraic coding theory and the construction of low-discrepancy sequences.

The purpose of this book is to revive some of the beautiful results obtained by various geometers of the 19th century, and to give its readers a taste of concrete algebraic geometry. A good deal of space is devoted to cross-ratios, conics, quadrics, and various interesting curves and surfaces. The fundamentals of projective geometry are efficiently dealt with by using a modest amount of linear algebra. An axiomatic characterization of projective planes is also given. While the topology of projective spaces over real and complex fields is described, and while the geometry of the complex projective libe is applied to the study of circles and Möbius transformations, the book is not restricted to these fields. Interesting properties of projective spaces, conics, and quadrics over finite fields are also given. This book is the first volume in the Readings in Mathematics sub-series of the UTM. From the reviews: "...The book of P. Samuel thus fills a gap in the literature. It is a little jewel. Starting from a minimal background in algebra, he succeeds in 160 pages in giving a coherent exposition of all of projective geometry. ... one reads this book like a novel. " D.Lazard in Gazette des Mathématiciens#1

This book is a visually compelling journey through the unique geometric discoveries of Frank Chester, a contemporary sacred geometer, artist, and sculptor. This art-style book with highly polished design elements leads the reader from discovery to discovery, complemented by original text from the author, a PhD who has studied Frank's work from its inception, when it was just seven sticks in a ball of mud on the banks of the American River... From the back cover: The ancient tradition of Sacred Geometry is still alive and well in the person of Frank Chester. He has discovered a new geometric form that unites the five Platonic solids and provides some startling indications about the form and function of the human heart. This new form, called the Chestahedron, was discovered in 2000, and is a seven-sided polyhedron with surfaces of equal area. Frank has been exploring the form and its significance for over a decade. His work has potential implications across a number of areas, from physiology to architecture, sculpture, geology, and beyond. Inspired by the work of Rudolf Steiner, Frank sees a deep connection between form and spirit. This book gives a brief, highly visual overview of some of Frank's discoveries, and presents a compelling series of indications for future research.

This book is a translation of an authoritative introductory text based on a lecture series delivered by the renowned differential geometer, Professor S S Chern in Beijing University in 1980. The original Chinese text, authored by Professor Chern and Professor Wei-Huan Chen, was a unique contribution to the mathematics literature, combining simplicity and economy of approach with depth of contents. The present translation is aimed at a wide audience, including (but not limited to) advanced undergraduate and graduate students in mathematics, as well as physicists interested in the diverse applications of differential geometry to physics. In addition to a thorough treatment of the fundamentals of manifold theory, exterior algebra, the exterior calculus, connections on fiber bundles, Riemannian geometry, Lie groups and moving frames, and complex manifolds (with a succinct introduction to the theory of Chern classes), and an appendix on the relationship between differential geometry and theoretical physics, this book includes a new chapter on Finsler geometry and a new appendix on the history and recent developments of differential geometry, the latter prepared specially for this edition by Professor Chern to bring the text into perspectives.

This lavishly illustrated book provides an unusually accessible approach to geometry by placing it in historical context. With concise discussions and carefully chosen illustrations the author brings the material to life by showing what problems motivated early geometers throughout the world. Geometry Civilized covers classical plane geometry, emphasizing the methods of Euclid but also drawing on advances made in China and India. It includes a wide range of problems, solutions, and illustrations, as well as a chapter on trigonometry, and prepares its readers for the study of solid geometry and conic sections.

This book is intended as an introductory text on the subject of Lie groups and algebras and their role in various fields of mathematics and physics. It is written by and for researchers who are primarily analysts or physicists, not algebraists or geometers. Not that we have eschewed the algebraic and geo­ metric developments. But we wanted to present them in a concrete way and to show how the subject interacted with physics, geometry, and mechanics. These interactions are, of course, manifold; we have discussed many of them here-in particular, Riemannian geometry, elementary particle physics, sym­ metries of differential equations, completely integrable Hamiltonian systems, and spontaneous symmetry breaking. Much ofthe material we have treated is standard and widely available; but we have tried to steer a course between the descriptive approach such as found in Gilmore and Wybourne, and the abstract mathematical approach of Helgason or Jacobson. Gilmore and Wybourne address themselves to the physics community whereas Helgason and Jacobson address themselves to the mathematical community. This book is an attempt to synthesize the two points of view and address both audiences simultaneously. We wanted to present the subject in a way which is at once intuitive, geometric, applications­ oriented, mathematically rigorous, and accessible to students and researchers without an extensive background in physics, algebra, or geometry.