Product Description: This unique book overturns our ideas about non-Euclidean geometry and the fine-structure constant, and attempts to solve long-standing mathematical problems. It describes a general theory of "recursive" hyperbolic functions based on the "Mathematics of Harmony," and the "golden," "silver," and other "metallic" proportions...read more

Product Description: The long-awaited new edition of a groundbreaking work on the impact of alternative concepts of space on modern art.In this groundbreaking study, first published in 1983 and unavailable for over a decade, Linda Dalrymple Henderson demonstrates that two concepts of space beyond immediate perception―the curved spaces of non-Euclidean geometry and, most important, a higher, fourth dimension of space―were central to the development of modern art...read more

Introduction to NON-EUCLIDEAN GEOMETRY by HAROLD E. WOLFE . PREFACE: This book has been written in an attempt to provide a satisfactory textbook to be used as a basis for elementary courses in Non-Euclid ean Geometry. The need for such a volume, definitely intended for classroom use and containing substantial lists of exercises, has been evident for some time. It is hoped that this one will meet the re quirements of those instructors who have been teaching the subject tegularly, and also that its appearance will encourage others to institute such courses. x The benefits and amenities of a formal study of Non-Euclidean Geometry are generally recognized. Not only is the subject matter itself valuable and intensely fascinating, well worth the time of any student of mathematics, but there is probably no elementary course which exhibits so clearly the nature and significance of geometry and, indeed, of mathematics in general. However, a mere cursory acquaintance with the subject will not do. One must follow its development at least a little way to see how things come out, and try his hand at demonstrating propositions under circumstances such that intuition no longer serves as a guide. For teachers and prospective teachers of geometry in the secondary schools the study of Non-Euclidean Geometry is invaluable. With out it there is strong likelihood that they will not understand the real nature of the subject they are teaching and the import of its applications to the interpretation of physical space. Among the first books on Non-Euclidean Geometry to appear in English was one, scarcely more than a pamphlet, written in 1880 by G. Chrystal. Even at that early date the value of this study for those preparing to teach was recognized. In the preface to this little brochure, Chrystal expressed his desire to bring pangeometrical speculations under the notice of those engaged in the teaching of geometry He wrote It will not be supposed that I advocate the introduction of pan geometry as a school subject it is for the teacher that I advocate such a study. It is a great mistake to suppose that it is sufficient for the teacher of an elementary subject to be just ahead of his pupils. No one can be a good elementary teacher who cannot handle his subject with the grasp of a master. Geometrical insight and wealth of geometrical ideas, either natural or acquired, are essential to a good teacher of geometry and I know of no better way of cultivat ing them than by studying pan geometry. Within recent years the number of American colleges and uni versities which offer courses in advanced Euclidean Geometry has increased rapidly. There is evidence that the quality of the teaching of geometry in our secondary schools has, accordingly, greatly improved. But advanced study in Euclidean Geometry is not the only requisite for the good teaching of Euclid. The study of Non-Euclidean Geometry takes its place beside it as an indispensable part of the training of a well-prepared teacher of high school geometry. This book has been prepared primarily for students who have completed a course in calculus. However, although some mathe matical maturity will be found helpful, much of it can be read profitably and with understanding by one who has completed a secondary school course in Euclidean Geometry. He need only omit Chapters V and VI, which make use of trigonometry and calcu lus, and the latter part of Chapter VII. In Chapters II and III, the historical background of the subject has been treated quite fully. It has been said that no subject, when separated from its history, loses more than mathematics. This is particularly true of Non-Euclidean Geometry...

Product Description: In the Corpus Aristotelicum there are 18 passages where it can be shown that Aristotle quotes statements that are formally opposite to the fundamental Euclidean theorem of the sum of the angles in a triangle. These statements are the result of the attempt by the geometricians of the Academy to prove the fundamental approach of Euclidean geometry indirectly...read more

Richard Trudeau confronts the fundamental question of truth and its representation through mathematical models in The Non-Euclidean Revolution. First, the author analyzes geometry in its historical and philosophical setting; second, he examines a revolution every bit as significant as the Copernican revolution in astronomy and the Darwinian revolution in biology; third, on the most speculative level, he questions the possibility of absolute knowledge of the world. Trudeau writes in a lively, entertaining, and highly accessible style. His book provides one of the most stimulating and personal presentations of a struggle with the nature of truth in mathematics and the physical world.

Product Description: Stahl's Second Edition continues to provide students with the elementary and constructive development of modern geometry that brings them closer to current geometric research. At the same time, repeated use is made of high school geometry, algebra, trigonometry, and calculus, thus reinforcing the students' understanding of these disciplines as well as enhancing their perception of mathematics as a unified endeavor...read more

``In this book Girolamo Saccheri set forth in 1733, for the first time ever, what amounts to the axiom systems of non-Euclidean geometry. It is in this book that, for the first time in history, theorem after theorem of (hyperbolic) non-Euclidean geometry is stated and proved. Why--one cannot help asking-did Saccheri not evaluate correctly what he had achieved, why did he not claim credit for the discovery of non-Euclidean geometry? ... The main content of the Notes are a series of annotations to Saccheri's text by the eminent scholars Paul Stackel and Friedrich Engel. These annotations originally appeared as footnotes to these authors' German translation of Euclides Vindicatus and were, with some modifications, translated into English by F. Steinhardt.'' --from the Preface to the Second English Edition

Product Description: This captivating book explains some of mathematics' most fascinating ideas to nonspecialists. It explores items of philosophical and historical interest, discusses the often-surprising applicability of mathematics, and reveals the subject's intrinsic beauty...read more

A guide for people in science, technology, or business, rather than for people intending to become professional technical writers. Discusses such aspects as the principles of communication, document design, correspondence, report strategies, seeking employment, and grammar. Also includes sections on such topics as writing on computers and ethics. Updated and reorganized from the 1993 edition. Annotation c. by Book News, Inc., Portland, Or.

Product Description: An account of the major work of Janos Bolyai, a nineteenth-century mathematician who set the stage for the field of non-Euclidean geometry.Janos Bolyai (1802-1860) was a mathematician who changed our fundamental ideas about space...read more

Numerous figures illustrate the geometric principles explained in this volume through the intuitive approach

Product Description: ###############################################################################################################################################################################################################################################################

(view table of contents)

Product Description: Based on lectures by a noted mathematician, this text offers an essential background in conformal representation. Subjects include the Möbius transformation, non-Euclidean geometry, elementary transformations, Schwarz's Lemma, transformation of the frontier and closed surfaces, and the general theorem of uniformization...read more

Product Description: The aim of this book is to throw light on various facets of geometry through development of four geometrical themes. The first theme is about the ellipse, the shape of the shadow cast by a circle. The next, a natural continuation of the first, is a study of all three types of conic sections, the ellipse, the parabola and the hyperbola...read more

Product Description: In the 1880s, over fifty years after the discovery of the hyperbolic plane, Poincare pointed out that this plane provides a very useful context for describing the properties of the solutions of an important class of differential equations...read more

Develops a simple non-Euclidean geometry and explores some of its practical applications through graphs, research problems, and exercises. Includes selected answers.