Problems and Solutions in Euclidean Geometry

Author: M. N. Aref,William Wernick

Publisher: Courier Corporation

ISBN: 0486477207

Category: Mathematics

Page: 258

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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.

Advanced Euclidean Geometry

Author: Roger A. Johnson

Publisher: Courier Corporation

ISBN: 048615498X

Category: Mathematics

Page: 336

View: 483

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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.

College Geometry

An Introduction to the Modern Geometry of the Triangle and the Circle

Author: Nathan Altshiller-Court

Publisher: Courier Corporation

ISBN: 0486141373

Category: Mathematics

Page: 336

View: 1200

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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.

Famous Problems of Geometry and How to Solve Them

Author: Benjamin Bold

Publisher: Courier Corporation

ISBN: 0486137635

Category: Science

Page: 144

View: 5178

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Delve into the development of modern mathematics and match wits with Euclid, Newton, Descartes, and others. Each chapter explores an individual type of challenge, with commentary and practice problems. Solutions.

Problem-Solving and Selected Topics in Euclidean Geometry

In the Spirit of the Mathematical Olympiads

Author: Sotirios E. Louridas,Michael Th. Rassias

Publisher: Springer Science & Business Media

ISBN: 1461472733

Category: Mathematics

Page: 235

View: 9699

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"Problem-Solving and Selected Topics in Euclidean Geometry: in the Spirit of the Mathematical Olympiads" contains theorems which are of particular value for the solution of geometrical problems. Emphasis is given in the discussion of a variety of methods, which play a significant role for the solution of problems in Euclidean Geometry. Before the complete solution of every problem, a key idea is presented so that the reader will be able to provide the solution. Applications of the basic geometrical methods which include analysis, synthesis, construction and proof are given. Selected problems which have been given in mathematical olympiads or proposed in short lists in IMO's are discussed. In addition, a number of problems proposed by leading mathematicians in the subject are included here. The book also contains new problems with their solutions. The scope of the publication of the present book is to teach mathematical thinking through Geometry and to provide inspiration for both students and teachers to formulate "positive" conjectures and provide solutions.

Taxicab Geometry

An Adventure in Non-Euclidean Geometry

Author: Eugene F. Krause

Publisher: Courier Corporation

ISBN: 048613606X

Category: Mathematics

Page: 96

View: 8001

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Fascinating, accessible introduction to unusual mathematical system in which distance is not measured by straight lines. Illustrated topics include applications to urban geography and comparisons to Euclidean geometry. Selected answers to problems.

Euclidean Geometry and Transformations

Author: Clayton W. Dodge

Publisher: Courier Corporation

ISBN: 0486138429

Category: Mathematics

Page: 304

View: 2573

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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.

Geometry in Problems

Author: Alexander Shen

Publisher: American Mathematical Soc.

ISBN: 1470419211

Category: Geometry

Page: 214

View: 7912

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Classical Euclidean geometry, with all its triangles, circles, and inscribed angles, remains an excellent playground for high-school mathematics students, even if it looks outdated from the professional mathematician's viewpoint. It provides an excellent choice of elegant and natural problems that can be used in a course based on problem solving. The book contains more than 750 (mostly) easy but nontrivial problems in all areas of plane geometry and solutions for most of them, as well as additional problems for self-study (some with hints). Each chapter also provides concise reminders of basic notions used in the chapter, so the book is almost self-contained (although a good textbook and competent teacher are always recommended). More than 450 figures illustrate the problems and their solutions. The book can be used by motivated high-school students, as well as their teachers and parents. After solving the problems in the book the student will have mastered the main notions and methods of plane geometry and, hopefully, will have had fun in the process. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession. What a joy! Shen's ``Geometry in Problems'' is a gift to the school teaching world. Beautifully organized by content topic, Shen has collated a vast collection of fresh, innovative, and highly classroom-relevant questions, problems, and challenges sure to enliven the minds and clever thinking of all those studying Euclidean geometry for the first time. This book is a spectacular resource for educators and students alike. Users will not only sharpen their mathematical understanding of specific topics but will also sharpen their problem-solving wits and come to truly own the mathematics explored. Also, Math Circle leaders can draw much inspiration for session ideas from the material presented in this book. --James Tanton, Mathematician-at-Large, Mathematical Association of America We learn mathematics best by doing mathematics. The author of this book recognizes this principle. He invites the reader to participate in learning plane geometry through carefully chosen problems, with brief explanations leading to much activity. The problems in the book are sometimes deep and subtle: almost everyone can do some of them, and almost no one can do all. The reader comes away with a view of geometry refreshed by experience. --Mark Saul, Director of Competitions, Mathematical Association of America

Geometry, Its Elements and Structure

Second Edition

Author: Alfred S. Posamentier,Robert L. Bannister

Publisher: Courier Corporation

ISBN: 0486492672

Category: Mathematics

Page: 624

View: 9964

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"Co-written by a bestselling high school and university textbook author, a longtime educational and standards pioneer, this up-to-date text is geared toward high school geometry classes and contains standard material for numerous state competencies. Topics include plane, solid, coordinate, vector, and non-Euclidean geometry. Features more than 2,000 illustrations, numerous examples with worked-out solutions, and supplementary reading. Electronic solutions manual and annotated teacher's edition are available. "--

Introduction to Non-Euclidean Geometry

Author: Harold E. Wolfe

Publisher: Courier Corporation

ISBN: 0486320375

Category: Mathematics

Page: 272

View: 6058

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College-level text for elementary courses covers the fifth postulate, hyperbolic plane geometry and trigonometry, and elliptic plane geometry and trigonometry. Appendixes offer background on Euclidean geometry. Numerous exercises. 1945 edition.

Differential Geometry

Author: Erwin Kreyszig

Publisher: Courier Corporation

ISBN: 0486318621

Category: Mathematics

Page: 384

View: 2226

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An introductory textbook on the differential geometry of curves and surfaces in 3-dimensional Euclidean space, presented in its simplest, most essential form. With problems and solutions. Includes 99 illustrations.

Geometry, Relativity and the Fourth Dimension

Author: Rudolf Rucker

Publisher: Courier Corporation

ISBN: 0486140334

Category: Science

Page: 160

View: 5467

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Exposition of fourth dimension, concepts of relativity as Flatland characters continue adventures. Topics include curved space time as a higher dimension, special relativity, and shape of space-time. Includes 141 illustrations.

Geometry: Euclid and Beyond

Author: Robin Hartshorne

Publisher: Springer Science & Business Media

ISBN: 0387226761

Category: Mathematics

Page: 528

View: 6457

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This book offers a unique opportunity to understand the essence of one of the great thinkers of western civilization. A guided reading of Euclid's Elements leads to a critical discussion and rigorous modern treatment of Euclid's geometry and its more recent descendants, with complete proofs. Topics include the introduction of coordinates, the theory of area, history of the parallel postulate, the various non-Euclidean geometries, and the regular and semi-regular polyhedra.

Classical Geometry

Euclidean, Transformational, Inversive, and Projective

Author: I. E. Leonard,J. E. Lewis,A. C. F. Liu,G. W. Tokarsky

Publisher: John Wiley & Sons

ISBN: 1118839439

Category: Mathematics

Page: 496

View: 9343

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Foundations of Geometry

Author: C. R. Wylie

Publisher: Courier Corporation

ISBN: 0486472140

Category: Education

Page: 338

View: 8919

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Explains geometric theories and shows many examples.

Challenging Problems in Geometry

Author: Alfred S. Posamentier,Charles T. Salkind

Publisher: Courier Corporation

ISBN: 0486134865

Category: Mathematics

Page: 256

View: 8331

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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.

Problem-Solving Strategies

Author: Arthur Engel

Publisher: Springer Science & Business Media

ISBN: 0387226419

Category: Mathematics

Page: 403

View: 6537

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A unique collection of competition problems from over twenty major national and international mathematical competitions for high school students. Written for trainers and participants of contests of all levels up to the highest level, this will appeal to high school teachers conducting a mathematics club who need a range of simple to complex problems and to those instructors wishing to pose a "problem of the week", thus bringing a creative atmosphere into the classrooms. Equally, this is a must-have for individuals interested in solving difficult and challenging problems. Each chapter starts with typical examples illustrating the central concepts and is followed by a number of carefully selected problems and their solutions. Most of the solutions are complete, but some merely point to the road leading to the final solution. In addition to being a valuable resource of mathematical problems and solution strategies, this is the most complete training book on the market.

Geometry: A Comprehensive Course

Author: Dan Pedoe

Publisher: Courier Corporation

ISBN: 0486131734

Category: Mathematics

Page: 464

View: 5904

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Introduction to vector algebra in the plane; circles and coaxial systems; mappings of the Euclidean plane; similitudes, isometries, Moebius transformations, much more. Includes over 500 exercises.

Lessons in Geometry: Plane geometry

Author: Jacques Hadamard

Publisher: American Mathematical Soc.

ISBN: 0821843672

Category: Mathematics

Page: 330

View: 750

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This is a work in the tradition of Euclidean synthetic geometry written by one of the 20th century's great mathematicians. The text starts where Euclid starts, and covers all the basics of plane Euclidean geometry.

Geometry by Construction

Object Creation and Problem-solving in Euclidean and Non-Euclidean Geometries

Author: Michael McDaniel

Publisher: Universal-Publishers

ISBN: 1627340289

Category: Geometrical constructions

Page: 150

View: 6573

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"'Geometry by construction' challenges its readers to participate in the creation of mathematics. The questions span the spectrum from easy to newly published research and so are appropriate for a variety of students and teachers. From differentiation in a high school course through college classes and into summer research, any interested geometer will find compelling material"--Back cover.