Download or read book A Vector Approach to Euclidean Geometry Vol 1 written by Herbert E. Vaughan and published by . This book was released on 1971 with total page 483 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Vector Approach to Euclidean Geometry written by Herbert Edward Vaughan and published by . This book was released on 1971 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Vector Approach to Euclidean Geometry Vector Spaces and Affine Geometry written by Herbert E.. Vaughan and published by . This book was released on 1971 with total page 483 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Vector Approach to Plane Euclidean Geometry written by David Lee Burke and published by . This book was released on 1967 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Vector Space Approach to Geometry written by Melvin Hausner and published by Courier Dover Publications. This book was released on 2018-10-17 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: A fascinating exploration of the correlation between geometry and linear algebra, this text also offers elementary explanations of the role of geometry in other branches of math and science. 1965 edition.
Download or read book Geometric Algebra for Computer Science written by Leo Dorst and published by Elsevier. This book was released on 2010-07-26 with total page 664 pages. Available in PDF, EPUB and Kindle. Book excerpt: Until recently, almost all of the interactions between objects in virtual 3D worlds have been based on calculations performed using linear algebra. Linear algebra relies heavily on coordinates, however, which can make many geometric programming tasks very specific and complex-often a lot of effort is required to bring about even modest performance enhancements. Although linear algebra is an efficient way to specify low-level computations, it is not a suitable high-level language for geometric programming. Geometric Algebra for Computer Science presents a compelling alternative to the limitations of linear algebra. Geometric algebra, or GA, is a compact, time-effective, and performance-enhancing way to represent the geometry of 3D objects in computer programs. In this book you will find an introduction to GA that will give you a strong grasp of its relationship to linear algebra and its significance for your work. You will learn how to use GA to represent objects and perform geometric operations on them. And you will begin mastering proven techniques for making GA an integral part of your applications in a way that simplifies your code without slowing it down. * The first book on Geometric Algebra for programmers in computer graphics and entertainment computing * Written by leaders in the field providing essential information on this new technique for 3D graphics * This full colour book includes a website with GAViewer, a program to experiment with GA
Download or read book Resources in Education written by and published by . This book was released on 1980-09 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Methods for Euclidean Geometry written by Owen Byer and published by American Mathematical Soc.. This book was released on 2010-12-31 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: Euclidean plane geometry is one of the oldest and most beautiful topics in mathematics. Instead of carefully building geometries from axiom sets, this book uses a wealth of methods to solve problems in Euclidean geometry. Many of these methods arose where existing techniques proved inadequate. In several cases, the new ideas used in solving specific problems later developed into independent areas of mathematics. This book is primarily a geometry textbook, but studying geometry in this way will also develop students' appreciation of the subject and of mathematics as a whole. For instance, despite the fact that the analytic method has been part of mathematics for four centuries, it is rarely a tool a student considers using when faced with a geometry problem. Methods for Euclidean Geometry explores the application of a broad range of mathematical topics to the solution of Euclidean problems.
Download or read book Euclidean Geometry written by Mark Solomonovich and published by iUniverse. This book was released on 2010 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is a self-contained presentation of Euclidean Geometry, a subject that has been a core part of school curriculum for centuries. The discussion is rigorous, axiom-based, written in a traditional manner, true to the Euclidean spirit. Transformations in the Euclidean plane are included as part of the axiomatics and as a tool for solving construction problems. The textbook can be used for teaching a high school or an introductory level college course. It can be especially recommended for schools with enriched mathematical programs and for homeschoolers looking for a rigorous traditional discussion of geometry. The text is supplied with over 1200 questions and problems, ranging from simple to challenging. The solutions sections of the book contain about 200 answers and hints to solutions and over 100 detailed solutions involving proofs and constructions. More solutions and some supplements for teachers are available in the Instructor's Manual, which is issued as a separate book. Book Reviews: 'In terms of presentation, this text is more rigorous than any existing high school textbook that I know of. It is based on a system of axioms that describe incidence, postulate a notion of congruence of line segments, and assume the existence of enough rigid motions ("free mobility")... My gut reaction to the book is, wouldn't it be wonderful if American high school students could be exposed to this serious mathematical treatment of elementary geometry, instead of all the junk that is presented to them in existing textbooks. This book makes no concession to the TV-generation of students who want (or is it the publishers who want it for them?) pretty pictures, side bars, puzzles, games, historical references, cartoons, and all those colored images that clutter the pages of a typical modern textbook, while the mathematical content is diluted more and more with each successive edition.' Professor Robin Hartshorne, University of California at Berkeley. 'The textbook "Euclidean Geometry" by Mark Solomonovich fills a big gap in the plethora of mathematical textbooks - it provides an exposition of classical geometry with emphasis on logic and rigorous proofs... I would be delighted to see this textbook used in Canadian schools in the framework of an improved geometry curriculum. Until this day comes, I highly recommend "Euclidean Geometry" by Mark Solomonovich to be used in Mathematics Enrichment Programs across Canada and the USA.' Professor Yuly Billig, Carlton University.
Download or read book Lectures on Euclidean Geometry Volume 1 written by Paris Pamfilos and published by Springer Nature. This book was released on 2024 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: Zusammenfassung: This is a comprehensive two-volumes text on plane and space geometry, transformations and conics, using a synthetic approach. The first volume focuses on Euclidean Geometry of the plane, and the second volume on Circle measurement, Transformations, Space geometry, Conics. The book is based on lecture notes from more than 30 courses which have been taught over the last 25 years. Using a synthetic approach, it discusses topics in Euclidean geometry ranging from the elementary (axioms and their first consequences), to the complex (the famous theorems of Pappus, Ptolemy, Euler, Steiner, Fermat, Morley, etc.). Through its coverage of a wealth of general and specialized subjects, it provides a comprehensive account of the theory, with chapters devoted to basic properties of simple planar and spatial shapes, transformations of the plane and space, and conic sections. As a result of repeated exposure of the material to students, it answers many frequently asked questions. Particular attention has been given to the didactic method; the text is accompanied by a plethora of figures (more than 2000) and exercises (more than 1400), most of them with solutions or expanded hints. Each chapter also includes numerous references to alternative approaches and specialized literature. The book is mainly addressed to students in mathematics, physics, engineering, school teachers in these areas, as well as, amateurs and lovers of geometry. Offering a sound and self-sufficient basis for the study of any possible problem in Euclidean geometry, the book can be used to support lectures to the most advanced level, or for self-study
Download or read book Catalog of Copyright Entries Third Series written by Library of Congress. Copyright Office and published by Copyright Office, Library of Congress. This book was released on 1973 with total page 1620 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Vector Geometry written by Gilbert De B. Robinson and published by Courier Corporation. This book was released on 2011-01-01 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: This concise undergraduate-level text explores the relationship between algebra and geometry. Topics include determinants and linear equations, matrices, linear transformations, projective geometry, geometry on the sphere, and much more. An elementary course in plane geometry is the sole requirement, and answers to the exercises appear at the end. 1962 edition.
Download or read book Methods of Geometry written by James T. Smith and published by John Wiley & Sons. This book was released on 2011-03-01 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: A practical, accessible introduction to advanced geometryExceptionally well-written and filled with historical andbibliographic notes, Methods of Geometry presents a practical andproof-oriented approach. The author develops a wide range ofsubject areas at an intermediate level and explains how theoriesthat underlie many fields of advanced mathematics ultimately leadto applications in science and engineering. Foundations, basicEuclidean geometry, and transformations are discussed in detail andapplied to study advanced plane geometry, polyhedra, isometries,similarities, and symmetry. An excellent introduction to advancedconcepts as well as a reference to techniques for use inindependent study and research, Methods of Geometry alsofeatures: Ample exercises designed to promote effective problem-solvingstrategies Insight into novel uses of Euclidean geometry More than 300 figures accompanying definitions and proofs A comprehensive and annotated bibliography Appendices reviewing vector and matrix algebra, least upperbound principle, and equivalence relations An Instructor's Manual presenting detailed solutions to all theproblems in the book is available upon request from the Wileyeditorial department.
Download or read book Fundamentals of Mathematics written by Heinrich Behnke and published by MIT Press. This book was released on 1974 with total page 708 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume II of a unique survey of the whole field of pure mathematics.
Download or read book Geometry in the Mathematics Curriculum written by National Council of Teachers of Mathematics and published by . This book was released on 1973 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Grassmann Algebra Volume 1 Foundations written by John Browne and published by John M Browne. This book was released on 2012-10-25 with total page 589 pages. Available in PDF, EPUB and Kindle. Book excerpt: Grassmann Algebra Volume 1: Foundations Exploring extended vector algebra with Mathematica Grassmann algebra extends vector algebra by introducing the exterior product to algebraicize the notion of linear dependence. With it, vectors may be extended to higher-grade entities: bivectors, trivectors, … multivectors. The extensive exterior product also has a regressive dual: the regressive product. The pair behaves a little like the Boolean duals of union and intersection. By interpreting one of the elements of the vector space as an origin point, points can be defined, and the exterior product can extend points into higher-grade located entities from which lines, planes and multiplanes can be defined. Theorems of Projective Geometry are simply formulae involving these entities and the dual products. By introducing the (orthogonal) complement operation, the scalar product of vectors may be extended to the interior product of multivectors, which in this more general case may no longer result in a scalar. The notion of the magnitude of vectors is extended to the magnitude of multivectors: for example, the magnitude of the exterior product of two vectors (a bivector) is the area of the parallelogram formed by them. To develop these foundational concepts, we need only consider entities which are the sums of elements of the same grade. This is the focus of this volume. But the entities of Grassmann algebra need not be of the same grade, and the possible product types need not be constricted to just the exterior, regressive and interior products. For example quaternion algebra is simply the Grassmann algebra of scalars and bivectors under a new product operation. Clifford, geometric and higher order hypercomplex algebras, for example the octonions, may be defined similarly. If to these we introduce Clifford's invention of a scalar which squares to zero, we can define entities (for example dual quaternions) with which we can perform elaborate transformations. Exploration of these entities, operations and algebras will be the focus of the volume to follow this. There is something fascinating about the beauty with which the mathematical structures that Hermann Grassmann discovered describe the physical world, and something also fascinating about how these beautiful structures have been largely lost to the mainstreams of mathematics and science. He wrote his seminal Ausdehnungslehre (Die Ausdehnungslehre. Vollständig und in strenger Form) in 1862. But it was not until the latter part of his life that he received any significant recognition for it, most notably by Gibbs and Clifford. In recent times David Hestenes' Geometric Algebra must be given the credit for much of the emerging awareness of Grassmann's innovation. In the hope that the book be accessible to scientists and engineers, students and professionals alike, the text attempts to avoid any terminology which does not make an essential contribution to an understanding of the basic concepts. Some familiarity with basic linear algebra may however be useful. The book is written using Mathematica, a powerful system for doing mathematics on a computer. This enables the theory to be cross-checked with computational explorations. However, a knowledge of Mathematica is not essential for an appreciation of Grassmann's beautiful ideas.
Download or read book Analytic Hyperbolic Geometry in N Dimensions written by Abraham Albert Ungar and published by CRC Press. This book was released on 2014-12-17 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: The concept of the Euclidean simplex is important in the study of n-dimensional Euclidean geometry. This book introduces for the first time the concept of hyperbolic simplex as an important concept in n-dimensional hyperbolic geometry. Following the emergence of his gyroalgebra in 1988, the author crafted gyrolanguage, the algebraic language t
