The Universe of Conics

From the ancient Greeks to 21st century developments

Author: Georg Glaeser,Hellmuth Stachel,Boris Odehnal

Publisher: Springer

ISBN: 3662454505

Category: Mathematics

Page: 488

View: 7570

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.
Posted in Mathematics

Ancient Greece

Author: Thomas R. Martin

Publisher: Yale University Press

ISBN: 0300190638

Category: History

Page: 256

View: 3710

DIVIn this compact yet comprehensive history of ancient Greece, Thomas R. Martin brings alive Greek civilization from its Stone Age roots to the fourth century B.C. Focusing on the development of the Greek city-state and the society, culture, and architecture of Athens in its Golden Age, Martin integrates political, military, social, and cultural history in a book that will appeal to students and general readers alike. Now in its second edition, this classic work now features new maps and illustrations, a new introduction, and updates throughout./divDIV /divDIV“A limpidly written, highly accessible, and comprehensive history of Greece and its civilizations from prehistory through the collapse of Alexander the Great’s empire. . . . A highly readable account of ancient Greece, particularly useful as an introductory or review text for the student or the general reader.�—Kirkus Reviews/divDIV /divDIV“A polished and informative work that will be useful for general readers and students.�—Daniel Tompkins, Temple University/divDIV/div
Posted in History

Observations and Predictions of Eclipse Times by Early Astronomers

Author: J.M. Steele

Publisher: Springer Science & Business Media

ISBN: 9401595283

Category: History

Page: 324

View: 6102

Eclipses have long been seen as important celestial phenomena, whether as omens affecting the future of kingdoms, or as useful astronomical events to help in deriving essential parameters for theories of the motion of the moon and sun. This is the first book to collect together all presently known records of timed eclipse observations and predictions from antiquity to the time of the invention of the telescope. In addition to cataloguing and assessing the accuracy of the various records, which come from regions as diverse as Ancient Mesopotamia, China, and Europe, the sources in which they are found are described in detail. Related questions such as what type of clocks were used to time the observations, how the eclipse predictions were made, and how these prediction schemes were derived from the available observations are also considered. The results of this investigation have important consequences for how we understand the relationship between observation and theory in early science and the role of astronomy in early cultures, and will be of interest to historians of science, astronomers, and ancient and medieval historians.
Posted in History

History of Western Philosophy

Collectors Edition

Author: Bertrand Russell

Publisher: Routledge

ISBN: 1135692912

Category: Philosophy

Page: 728

View: 6151

Now in a special gift edition, and featuring a brand new foreword by Anthony Gottlieb, this is a dazzlingly unique exploration of the works of significant philosophers throughout the ages and a definitive must-have title that deserves a revered place on every bookshelf.
Posted in Philosophy

Lattice Theory: Foundation

Author: George Grätzer

Publisher: Springer Science & Business Media

ISBN: 9783034800181

Category: Mathematics

Page: 614

View: 7119

This book started with Lattice Theory, First Concepts, in 1971. Then came General Lattice Theory, First Edition, in 1978, and the Second Edition twenty years later. Since the publication of the first edition in 1978, General Lattice Theory has become the authoritative introduction to lattice theory for graduate students and the standard reference for researchers. The First Edition set out to introduce and survey lattice theory. Some 12,000 papers have been published in the field since then; so Lattice Theory: Foundation focuses on introducing the field, laying the foundation for special topics and applications. Lattice Theory: Foundation, based on the previous three books, covers the fundamental concepts and results. The main topics are distributivity, congruences, constructions, modularity and semimodularity, varieties, and free products. The chapter on constructions is new, all the other chapters are revised and expanded versions from the earlier volumes. Almost 40 “diamond sections’’, many written by leading specialists in these fields, provide a brief glimpse into special topics beyond the basics. “Lattice theory has come a long way... For those who appreciate lattice theory, or who are curious about its techniques and intriguing internal problems, Professor Grätzer's lucid new book provides a most valuable guide to many recent developments. Even a cursory reading should provide those few who may still believe that lattice theory is superficial or naive, with convincing evidence of its technical depth and sophistication.” Bulletin of the American Mathematical Society “Grätzer’s book General Lattice Theory has become the lattice theorist’s bible.” Mathematical Reviews
Posted in Mathematics

Symmetry and Pattern in Projective Geometry

Author: Eric Lord

Publisher: Springer Science & Business Media

ISBN: 144714631X

Category: Mathematics

Page: 184

View: 8650

Symmetry and Pattern in Projective Geometry is a self-contained study of projective geometry which compares and contrasts the analytic and axiomatic methods. The analytic approach is based on homogeneous coordinates, and brief introductions to Plücker coordinates and Grassmann coordinates are presented. This book looks carefully at linear, quadratic, cubic and quartic figures in two, three and higher dimensions. It deals at length with the extensions and consequences of basic theorems such as those of Pappus and Desargues. The emphasis throughout is on special configurations that have particularly interesting symmetry properties. The intricate and novel ideas of ‘Donald’ Coxeter, who is considered one of the great geometers of the twentieth century, are also discussed throughout the text. The book concludes with a useful analysis of finite geometries and a description of some of the remarkable configurations discovered by Coxeter. This book will be appreciated by mathematics students and those wishing to learn more about the subject of geometry. It makes accessible subjects and theorems which are often considered quite complicated and presents them in an easy-to-read and enjoyable manner.
Posted in Mathematics

Celestial Treasury

From the Music of the Spheres to the Conquest of Space

Author: Marc Lachièze-Rey,Jean-Pierre Luminet,Bibliothèque Nationale de France. Paris

Publisher: Cambridge University Press

ISBN: 9780521800402

Category: Art

Page: 207

View: 6517

A breathtaking survey of the richness of astronomical theories and illustrations through the ages.
Posted in Art

It's Been a Good Life

Author: Isaac Asimov

Publisher: Prometheus Books

ISBN: 1615921931

Category: Biography & Autobiography

Page: N.A

View: 1569

...fascinating...this readable and idiosyncratic self-portrait should attract a whole new generation of readers to Asimov's fine creative works. --Publishers WeeklyNew one-volume autobiography spans Asimov's life for the first time!As one of the most gifted and prolific writers of the twentieth century, Isaac Asimov became legendary for his inexhaustible creativity, wide-ranging intellectual curiosity, and talent for explaining complex subjects in clear, concise prose. While regaling his readers with an incredible opus of almost five hundred entertaining and illuminating science fiction and nonfiction books, he also found time to write a three-volume autobiography. Now these volumes have been condensed into one by Asimov's wife, Janet, who also shares excerpts from letters he wrote to her. Together these writings provide an intimate portrait of a creative genius whose love of learning and playing with ideas is evident on every page.Reading this autobiography is like sitting down with Isaac Asimov and experiencing his witty, engaging, and brilliant personality firsthand. We are treated to many marvelous stories about his upbringing in Depression-era Brooklyn, his early fascination with the new science fiction pulp magazines, the thrill of his first published story, the creation of his well-known story Nightfall, the genesis of the Foundation series, and the evolution of his creative life as a writer.He also reveals his inner thoughts about and experiences with various luminaries in science and science fiction. Above all, Asimov's autobiography conveys unbounded enthusiasm for his craft, the infectious joy of learning and creating, complete intellectual honesty, his strong humanist convictions, and his infinite fund of good humor and optimism even at the end of his life - all told in the lively clear writing style that was his trademark.Although Janet Jeppson Asimov concludes this work with a shocking revelation about her husband's death, the volume is clearly intended as a celebration - as the title suggests - of a wonderful, creative life. As a poignant coda to this work, Janet has appended one short story that was Isaac's favorite, and his 400th essay on this thoughts about science.Janet Jeppson Asimov, M.D. (New York, NY), a retired physician, is the author of twenty books and many short stories and articles. She currently writes a bimonthly science column for a newspaper syndicate.
Posted in Biography & Autobiography

The Language of Mathematics

Making the Invisible Visible

Author: Keith Devlin

Publisher: Macmillan

ISBN: 9780805072549

Category: Mathematics

Page: 352

View: 4869

"The great book of nature," said Galileo, "can be read only by those who know the language in which it was written. And this language is mathematics." In The Language of Mathematics, award-winning author Keith Devlin reveals the vital role mathematics plays in our eternal quest to understand who we are and the world we live in. More than just the study of numbers, mathematics provides us with the eyes to recognize and describe the hidden patterns of life—patterns that exist in the physical, biological, and social worlds without, and the realm of ideas and thoughts within. Taking the reader on a wondrous journey through the invisible universe that surrounds us—a universe made visible by mathematics—Devlin shows us what keeps a jumbo jet in the air, explains how we can see and hear a football game on TV, allows us to predict the weather, the behavior of the stock market, and the outcome of elections. Microwave ovens, telephone cables, children's toys, pacemakers, automobiles, and computers—all operate on mathematical principles. Far from a dry and esoteric subject, mathematics is a rich and living part of our culture. An exploration of an often woefully misunderstood subject, The Language of Mathematics celebrates the simplicity, the precision, the purity, and the elegance of mathematics.
Posted in Mathematics

Analytical Conics

Author: Barry Spain

Publisher: Courier Corporation

ISBN: 0486457737

Category: Mathematics

Page: 145

View: 7106

This concise text introduces students to analytical geometry, covering basic ideas and methods. Readily intelligible to any student with a sound mathematical background, it is designed both for undergraduates and for math majors. It will prove particularly valuable in preparing readers for more advanced treatments. The text begins with an overview of the analytical geometry of the straight line, circle, and the conics in their standard forms. It proceeds to discussions of translations and rotations of axes, and of the general equation of the second degree. The concept of the line at infinity is introduced, and the main properties of conics and pencils of conics are derived from the general equation. The fundamentals of cross-ratio, homographic correspondence, and line-coordinates are explored, including applications of the latter to focal properties. The final chapter provides a compact account of generalized homogeneous coordinates, and a helpful appendix presents solutions to many of the examples.
Posted in Mathematics

Geometric Methods and Applications

For Computer Science and Engineering

Author: Jean Gallier

Publisher: Springer Science & Business Media

ISBN: 1461301378

Category: Mathematics

Page: 566

View: 1710

As an introduction to fundamental geometric concepts and tools needed for solving problems of a geometric nature using a computer, this book fills the gap between standard geometry books, which are primarily theoretical, and applied books on computer graphics, computer vision, or robotics that do not cover the underlying geometric concepts in detail. Gallier offers an introduction to affine, projective, computational, and Euclidean geometry, basics of differential geometry and Lie groups, and explores many of the practical applications of geometry. Some of these include computer vision, efficient communication, error correcting codes, cryptography, motion interpolation, and robot kinematics. This comprehensive text covers most of the geometric background needed for conducting research in computer graphics, geometric modeling, computer vision, and robotics and as such will be of interest to a wide audience including computer scientists, mathematicians, and engineers.
Posted in Mathematics

Mathematics Across Cultures

The History of Non-Western Mathematics

Author: Helaine Selin

Publisher: Springer Science & Business Media

ISBN: 9401143013

Category: Mathematics

Page: 479

View: 3142

Mathematics Across Cultures: A History of Non-Western Mathematics consists of essays dealing with the mathematical knowledge and beliefs of cultures outside the United States and Europe. In addition to articles surveying Islamic, Chinese, Native American, Aboriginal Australian, Inca, Egyptian, and African mathematics, among others, the book includes essays on Rationality, Logic and Mathematics, and the transfer of knowledge from East to West. The essays address the connections between science and culture and relate the mathematical practices to the cultures which produced them. Each essay is well illustrated and contains an extensive bibliography. Because the geographic range is global, the book fills a gap in both the history of science and in cultural studies. It should find a place on the bookshelves of advanced undergraduate students, graduate students, and scholars, as well as in libraries serving those groups.
Posted in Mathematics

The Poincare Conjecture

In Search of the Shape of the Universe

Author: Donal O'Shea

Publisher: Bloomsbury Publishing USA

ISBN: 9780802718945

Category: Mathematics

Page: 304

View: 3556

Henri Poincaré was one of the greatest mathematicians of the late nineteenth and early twentieth century. He revolutionized the field of topology, which studies properties of geometric configurations that are unchanged by stretching or twisting. The Poincaré conjecture lies at the heart of modern geometry and topology, and even pertains to the possible shape of the universe. The conjecture states that there is only one shape possible for a finite universe in which every loop can be contracted to a single point. Poincaré's conjecture is one of the seven "millennium problems" that bring a one-million-dollar award for a solution. Grigory Perelman, a Russian mathematician, has offered a proof that is likely to win the Fields Medal, the mathematical equivalent of a Nobel prize, in August 2006. He also will almost certainly share a Clay Institute millennium award. In telling the vibrant story of The Poincaré Conjecture, Donal O'Shea makes accessible to general readers for the first time the meaning of the conjecture, and brings alive the field of mathematics and the achievements of generations of mathematicians whose work have led to Perelman's proof of this famous conjecture.
Posted in Mathematics

The Reception of Darwinism in the Iberian World

Spain, Spanish America, and Brazil

Author: T.F Glick

Publisher: Springer Science & Business Media

ISBN: 9781402000829

Category: History

Page: 272

View: 8130

This book provides both for academic historians and the general reader a broad perspective on Darwin's impact in the Spanish- and Portuguese-speaking worlds. In Latin American countries with black and Amerindian populations, evolutionary theory was quickly mobilized for theorizing racial differences, while in Spain attention was focused on class differentiation, explained by a series of Darwinian, Social Darwinist, and Eugenic hypotheses. The wide variety of approaches to evolutionary and social theory in countries whose culture was very similar points illuminates those issues thought to be of particular significance for national identity, whether political, ethnic, or racial.
Posted in History

The Shape of Inner Space

String Theory and the Geometry of the Universe's Hidden Dimensions

Author: Shing-Tung Yau,Steve Nadis

Publisher: Basic Books

ISBN: 0465022669

Category: Science

Page: 400

View: 602

String theory says we live in a ten-dimensional universe, but that only four are accessible to our everyday senses. According to theorists, the missing six are curled up in bizarre structures known as Calabi-Yau manifolds. In The Shape of Inner Space, Shing-Tung Yau, the man who mathematically proved that these manifolds exist, argues that not only is geometry fundamental to string theory, it is also fundamental to the very nature of our universe. Time and again, where Yau has gone, physics has followed. Now for the first time, readers will follow Yau’s penetrating thinking on where we’ve been, and where mathematics will take us next. A fascinating exploration of a world we are only just beginning to grasp, The Shape of Inner Space will change the way we consider the universe on both its grandest and smallest scales.
Posted in Science

A Cultural History of Physics

Author: Károly Simonyi

Publisher: CRC Press

ISBN: 1439865116

Category: Mathematics

Page: 636

View: 5676

While the physical sciences are a continuously evolving source of technology and of understanding about our world, they have become so specialized and rely on so much prerequisite knowledge that for many people today the divide between the sciences and the humanities seems even greater than it was when C. P. Snow delivered his famous 1959 lecture, "The Two Cultures." In A Cultural History of Physics, Hungarian scientist and educator Károly Simonyi succeeds in bridging this chasm by describing the experimental methods and theoretical interpretations that created scientific knowledge, from ancient times to the present day, within the cultural environment in which it was formed. Unlike any other work of its kind, Simonyi’s seminal opus explores the interplay of science and the humanities to convey the wonder and excitement of scientific development throughout the ages. These pages contain an abundance of excerpts from original resources, a wide array of clear and straightforward explanations, and an astonishing wealth of insight, revealing the historical progress of science and inviting readers into a dialogue with the great scientific minds that shaped our current understanding of physics. Beautifully illustrated, accurate in its scientific content and broad in its historical and cultural perspective, this book will be a valuable reference for scholars and an inspiration to aspiring scientists and humanists who believe that science is an integral part of our culture.
Posted in Mathematics

Points and Lines

Characterizing the Classical Geometries

Author: Ernest E. Shult

Publisher: Springer Science & Business Media

ISBN: 9783642156274

Category: Mathematics

Page: 676

View: 7145

The classical geometries of points and lines include not only the projective and polar spaces, but similar truncations of geometries naturally arising from the groups of Lie type. Virtually all of these geometries (or homomorphic images of them) are characterized in this book by simple local axioms on points and lines. Simple point-line characterizations of Lie incidence geometries allow one to recognize Lie incidence geometries and their automorphism groups. These tools could be useful in shortening the enormously lengthy classification of finite simple groups. Similarly, recognizing ruled manifolds by axioms on light trajectories offers a way for a physicist to recognize the action of a Lie group in a context where it is not clear what Hamiltonians or Casimir operators are involved. The presentation is self-contained in the sense that proofs proceed step-by-step from elementary first principals without further appeal to outside results. Several chapters have new heretofore unpublished research results. On the other hand, certain groups of chapters would make good graduate courses. All but one chapter provide exercises for either use in such a course, or to elicit new research directions.
Posted in Mathematics

Sheaf Theory

Author: Glen E. Bredon

Publisher: Springer Science & Business Media

ISBN: 9780387949055

Category: Mathematics

Page: 502

View: 3840

This book is primarily concerned with the study of cohomology theories of general topological spaces with "general coefficient systems." The parts of sheaf theory covered here are those areas important to algebraic topology. There are several innovations in this book. The concept of the "tautness" of a subspace is introduced and exploited throughout the book. The fact that sheaf theoretic cohomology satisfies the homotopy property is proved for general topological spaces. Relative cohomology is introduced into sheaf theory. The reader should have a thorough background in elementary homological algebra and in algebraic topology. A list of exercises at the end of each chapter will help the student to learn the material, and solutions of many of the exercises are given in an appendix. The new edition of this classic in the field has been substantially rewritten with the addition of over 80 examples and of further explanatory material. Among the items added are new sections on Cech cohomology, the Oliver transfer, intersection theory, generalized manifolds, locally homogeneous spaces, homological fibrations and
Posted in Mathematics

Science, Technology and Society in Contemporary Japan

Author: Morris Low,Shigeru Nakayama,Hitoshi Yoshioka

Publisher: Cambridge University Press

ISBN: 9780521654258

Category: History

Page: 226

View: 3632

This book explores the dynamic relationship between science, technology and Japanese society, examining how it has contributed to economic growth and national well-being. It presents a synthesis of recent debates by juxtaposing competing views about the role and direction of science, technology and medical care in Japan. Topics discussed include government policy, the private sector and community responses; computers and communication; the automobile industry, the aerospace industry and quality control; the environment; consumer electronics; medical care; and the role of gender. This is an ideal introductory text for students in the sociology of science and technology, the history and philosophy of science, and Japanese studies. Up-to-date research and case studies make this an invaluable resource for readers interested in the nature of science and technology in the twenty-first century.
Posted in History