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Author : Roger A. Johnson
Publisher : Courier Corporation
Page : 338 pages
File Size : 55,9 Mb
Release : 2013-01-08
Category : Mathematics
ISBN : 9780486154985
This classic text explores the geometry of the triangle and the circle, concentrating on extensions of Euclidean theory, and examining in detail many relatively recent theorems. 1929 edition.
Author : Gerard A. Venema
Publisher : American Mathematical Soc.
Page : 147 pages
File Size : 45,5 Mb
Release : 2013-12-31
Category : Mathematics
ISBN : 9780883857847
This book provides an inquiry-based introduction to advanced Euclidean geometry. It utilizes dynamic geometry software, specifically GeoGebra, to explore the statements and proofs of many of the most interesting theorems in the subject. Topics covered include triangle centers, inscribed, circumscribed, and escribed circles, medial and orthic triangles, the nine-point circle, duality, and the theorems of Ceva and Menelaus, as well as numerous applications of those theorems. The final chapter explores constructions in the Poincare disk model for hyperbolic geometry. The book can be used either as a computer laboratory manual to supplement an undergraduate course in geometry or as a stand-alone introduction to advanced topics in Euclidean geometry. The text consists almost entirely of exercises (with hints) that guide students as they discover the geometric relationships for themselves. First the ideas are explored at the computer and then those ideas are assembled into a proof of the result under investigation. The goals are for the reader to experience the joy of discovering geometric relationships, to develop a deeper understanding of geometry, and to encourage an appreciation for the beauty of Euclidean geometry.
Author : M. N. Aref,William Wernick
Publisher : Courier Corporation
Page : 274 pages
File Size : 42,8 Mb
Release : 2010-01-01
Category : Mathematics
ISBN : 9780486477206
Based on classical principles, this book is intended for a second course in Euclidean geometry and can be used as a refresher. Each chapter covers a different aspect of Euclidean geometry, lists relevant theorems and corollaries, and states and proves many propositions. Includes more than 200 problems, hints, and solutions. 1968 edition.
Author : C. Zwikker
Publisher : Courier Corporation
Page : 316 pages
File Size : 51,9 Mb
Release : 2011-11-30
Category : Mathematics
ISBN : 9780486153438
"Of chief interest to mathematicians, but physicists and others will be fascinated ... and intrigued by the fruitful use of non-Cartesian methods. Students ... should find the book stimulating." — British Journal of Applied Physics This study of many important curves, their geometrical properties, and their applications features material not customarily treated in texts on synthetic or analytic Euclidean geometry. Its wide coverage, which includes both algebraic and transcendental curves, extends to unusual properties of familiar curves along with the nature of lesser known curves. Informative discussions of the line, circle, parabola, ellipse, and hyperbola presuppose only the most elementary facts. The less common curves — cissoid, strophoid, spirals, the leminscate, cycloid, epicycloid, cardioid, and many others — receive introductions that explain both their basic and advanced properties. Derived curves-the involute, evolute, pedal curve, envelope, and orthogonal trajectories-are also examined, with definitions of their important applications. These range through the fields of optics, electric circuit design, hydraulics, hydrodynamics, classical mechanics, electromagnetism, crystallography, gear design, road engineering, orbits of subatomic particles, and similar areas in physics and engineering. The author represents the points of the curves by complex numbers, rather than the real Cartesian coordinates, an approach that permits simple, direct, and elegant proofs.
Author : Clayton W. Dodge
Publisher : Courier Corporation
Page : 306 pages
File Size : 55,7 Mb
Release : 2012-04-26
Category : Mathematics
ISBN : 9780486138428
This introduction to Euclidean geometry emphasizes transformations, particularly isometries and similarities. Suitable for undergraduate courses, it includes numerous examples, many with detailed answers. 1972 edition.
Author : Roger Arthur Johnson
Publisher : Unknown
Page : 344 pages
File Size : 52,5 Mb
Release : 1929
Category : Circle
ISBN : WISC:89043163211
Author : Alfred S. Posamentier,Charles T. Salkind
Publisher : Courier Corporation
Page : 275 pages
File Size : 48,5 Mb
Release : 2012-04-30
Category : Mathematics
ISBN : 9780486134864
Collection of nearly 200 unusual problems dealing with congruence and parallelism, the Pythagorean theorem, circles, area relationships, Ptolemy and the cyclic quadrilateral, collinearity and concurrency and more. Arranged in order of difficulty. Detailed solutions.
Author : Evan Chen
Publisher : American Mathematical Soc.
Page : 311 pages
File Size : 51,7 Mb
Release : 2021-08-23
Category : Education
ISBN : 9781470466206
This is a challenging problem-solving book in Euclidean geometry, assuming nothing of the reader other than a good deal of courage. Topics covered included cyclic quadrilaterals, power of a point, homothety, triangle centers; along the way the reader will meet such classical gems as the nine-point circle, the Simson line, the symmedian and the mixtilinear incircle, as well as the theorems of Euler, Ceva, Menelaus, and Pascal. Another part is dedicated to the use of complex numbers and barycentric coordinates, granting the reader both a traditional and computational viewpoint of the material. The final part consists of some more advanced topics, such as inversion in the plane, the cross ratio and projective transformations, and the theory of the complete quadrilateral. The exposition is friendly and relaxed, and accompanied by over 300 beautifully drawn figures. The emphasis of this book is placed squarely on the problems. Each chapter contains carefully chosen worked examples, which explain not only the solutions to the problems but also describe in close detail how one would invent the solution to begin with. The text contains a selection of 300 practice problems of varying difficulty from contests around the world, with extensive hints and selected solutions. This book is especially suitable for students preparing for national or international mathematical olympiads or for teachers looking for a text for an honor class.
Author : Alfred S. Posamentier
Publisher : Springer Science & Business Media
Page : 276 pages
File Size : 41,7 Mb
Release : 2002-07-12
Category : Mathematics
ISBN : 1930190859
Advanced Euclidean Geometry provides a thorough review of the essentials of high school geometry and then expands those concepts to advanced Euclidean geometry, to give teachers more confidence in guiding student explorations and questions. The text contains hundreds of illustrations created in The Geometer's Sketchpad Dynamic Geometry® software. It is packaged with a CD-ROM containing over 100 interactive sketches using SketchpadTM (assumes that the user has access to the program).
Author : Nathan Altshiller-Court
Publisher : Dover Publications
Page : 336 pages
File Size : 45,6 Mb
Release : 2013-12-30
Category : Electronic
ISBN : 0486788474
The standard university-level text for decades, this volume offers exercises in construction problems, harmonic division, circle and triangle geometry, and other areas. 1952 edition, revised and enlarged by the author.
Author : Edwin E. Moise
Publisher : Addison Wesley
Page : 520 pages
File Size : 40,8 Mb
Release : 1990
Category : Business & Economics
ISBN : UOM:39015053947407
Students can rely on Moise's clear and thorough presentation of basic geometry theorems. The author assumes that students have no previous knowledge of the subject and presents the basics of geometry from the ground up. This comprehensive approach gives instructors flexibility in teaching. For example, an advanced class may progress rapidly through Chapters 1-7 and devote most of its time to the material presented in Chapters 8, 10, 14, 19, and 20. Similarly, a less advanced class may go carefully through Chapters 1-7, and omit some of the more difficult chapters, such as 20 and 24.
Author : Roger A. Johnson
Publisher : Unknown
Page : 332 pages
File Size : 44,5 Mb
Release : 1960
Category : Geometry, Modern
ISBN : OCLC:819977377
Author : Owen Byer,Felix Lazebnik,Deirdre L. Smeltzer
Publisher : American Mathematical Soc.
Page : 461 pages
File Size : 49,5 Mb
Release : 2010-12-31
Category : Mathematics
ISBN : 9780883857632
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.
Author : C. R. Wylie
Publisher : Courier Corporation
Page : 578 pages
File Size : 44,5 Mb
Release : 2011-09-12
Category : Mathematics
ISBN : 9780486141701
This lucid introductory text offers both an analytic and an axiomatic approach to plane projective geometry. The analytic treatment builds and expands upon students' familiarity with elementary plane analytic geometry and provides a well-motivated approach to projective geometry. Subsequent chapters explore Euclidean and non-Euclidean geometry as specializations of the projective plane, revealing the existence of an infinite number of geometries, each Euclidean in nature but characterized by a different set of distance- and angle-measurement formulas. Outstanding pedagogical features include worked-through examples, introductions and summaries for each topic, and numerous theorems, proofs, and exercises that reinforce each chapter's precepts. Two helpful indexes conclude the text, along with answers to all odd-numbered exercises. In addition to its value to undergraduate students of mathematics, computer science, and secondary mathematics education, this volume provides an excellent reference for computer science professionals.
Author : Andreĭ Petrovich Kiselev
Publisher : Unknown
Page : 192 pages
File Size : 44,5 Mb
Release : 2008
Category : Geometry
ISBN : UCSD:31822037285152
This volume completes the English adaptation of a classical Russian textbook in elementary Euclidean geometry. The 1st volume subtitled "Book I. Planimetry" was published in 2006 (ISBN 0977985202). This 2nd volume (Book II. Stereometry) covers solid geometry, and contains a chapter on vectors, foundations, and introduction in non-Euclidean geometry added by the translator. The book intended for high-school and college students, and their teachers. Includes 317 exercises, index, and bibliography.
