Problems and Solutions in Euclidean Geometry

Author: M. N. Aref,William Wernick

Publisher: Courier Corporation

ISBN: 0486477207

Category: Mathematics

Page: 258

View: 2349

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.
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Advanced Euclidean Geometry

Author: Roger A. Johnson

Publisher: Courier Corporation

ISBN: 048615498X

Category: Mathematics

Page: 336

View: 5593

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.
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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: 4489

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.
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Famous Problems of Geometry and How to Solve Them

Author: Benjamin Bold

Publisher: Courier Corporation

ISBN: 0486137635

Category: Science

Page: 144

View: 7894

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.
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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: 8760

"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.
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Euclidean Geometry and Transformations

Author: Clayton W. Dodge

Publisher: Courier Corporation

ISBN: 0486138429

Category: Mathematics

Page: 304

View: 4915

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.
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Taxicab Geometry

An Adventure in Non-Euclidean Geometry

Author: Eugene F. Krause

Publisher: Courier Corporation

ISBN: 048613606X

Category: Mathematics

Page: 96

View: 6889

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.
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Geometry, Relativity and the Fourth Dimension

Author: Rudolf Rucker

Publisher: Courier Corporation

ISBN: 0486140334

Category: Science

Page: 160

View: 5648

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.
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Differential Geometry

Author: Erwin Kreyszig

Publisher: Courier Corporation

ISBN: 0486318621

Category: Mathematics

Page: 384

View: 665

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.
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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: 3374

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Challenging Problems in Geometry

Author: Alfred S. Posamentier,Charles T. Salkind

Publisher: Courier Corporation

ISBN: 0486134865

Category: Mathematics

Page: 256

View: 326

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.
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Introduction to Non-Euclidean Geometry

Author: Harold E. Wolfe

Publisher: Courier Corporation

ISBN: 0486320375

Category: Mathematics

Page: 272

View: 9779

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.
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Geometry: Euclid and Beyond

Author: Robin Hartshorne

Publisher: Springer Science & Business Media

ISBN: 0387226761

Category: Mathematics

Page: 528

View: 5732

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.
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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: 2345

"'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.
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Euclidean Geometry

A First Course

Author: Mark Solomonovich

Publisher: iUniverse

ISBN: 1440153485

Category: Education

Page: 408

View: 4292

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. From the 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.
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Philosophy of Mathematics and Deductive Structure in Euclid's Elements

Author: Ian Mueller

Publisher: Courier Corporation

ISBN: 0486150879

Category: Mathematics

Page: 400

View: 3855

This text provides an understanding of the classical Greek conception of mathematics as expressed in Euclid's Elements. It focuses on philosophical, foundational, and logical questions and features helpful appendixes.
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Solving Mathematical Problems

A Personal Perspective

Author: Terence Tao

Publisher: OUP Oxford

ISBN: 0199205612

Category: Mathematics

Page: 103

View: 900

Authored by a leading name in mathematics, this engaging and clearly presented text leads the reader through the tactics involved in solving mathematical problems at the Mathematical Olympiad level. With numerous exercises and assuming only basic mathematics, this text is ideal for students of14 years and above in pure mathematics.
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Lessons in Geometry: Plane geometry

Author: Jacques Hadamard

Publisher: American Mathematical Soc.

ISBN: 0821843672

Category: Mathematics

Page: 330

View: 2647

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.
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Geometry in Problems

Author: Alexander Shen

Publisher: American Mathematical Soc.

ISBN: 1470419211

Category: Geometry

Page: 214

View: 1374

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
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Foundations and Fundamental Concepts of Mathematics

Author: Howard Eves

Publisher: Courier Corporation

ISBN: 048613220X

Category: Mathematics

Page: 368

View: 6744

Third edition of popular undergraduate-level text offers historic overview, readable treatment of mathematics before Euclid, Euclid's Elements, non-Euclidean geometry, algebraic structure, formal axiomatics, sets, more. Problems, some with solutions. Bibliography.
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