Search Results for "problems-and-solutions-in-euclidean-geometry-dover-books-on-mathematics"

Problems and Solutions in Euclidean Geometry

Problems and Solutions in Euclidean Geometry

  • Author: M. N. Aref,William Wernick
  • Publisher: Courier Corporation
  • ISBN: 0486477207
  • Category: Mathematics
  • Page: 258
  • View: 7051
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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

Advanced Euclidean Geometry

  • Author: Roger A. Johnson
  • Publisher: Courier Corporation
  • ISBN: 048615498X
  • Category: Mathematics
  • Page: 336
  • View: 746
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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

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: 7319
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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

Famous Problems of Geometry and How to Solve Them

  • Author: Benjamin Bold
  • Publisher: Courier Corporation
  • ISBN: 0486137635
  • Category: Science
  • Page: 144
  • View: 1176
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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

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: 1601
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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

Taxicab Geometry

An Adventure in Non-Euclidean Geometry

  • Author: Eugene F. Krause
  • Publisher: Courier Corporation
  • ISBN: 048613606X
  • Category: Mathematics
  • Page: 96
  • View: 997
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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

Euclidean Geometry and Transformations

  • Author: Clayton W. Dodge
  • Publisher: Courier Corporation
  • ISBN: 0486138429
  • Category: Mathematics
  • Page: 304
  • View: 7734
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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

Geometry in Problems

  • Author: Alexander Shen
  • Publisher: American Mathematical Soc.
  • ISBN: 1470419211
  • Category: Geometry
  • Page: 214
  • View: 4821
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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

Differential Geometry

Differential Geometry

  • Author: Erwin Kreyszig
  • Publisher: Courier Corporation
  • ISBN: 0486318621
  • Category: Mathematics
  • Page: 384
  • View: 1959
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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

Geometry, Relativity and the Fourth Dimension

  • Author: Rudolf Rucker
  • Publisher: Courier Corporation
  • ISBN: 0486140334
  • Category: Science
  • Page: 160
  • View: 1967
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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.

Classical Geometry

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: 883
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Introduction to Non-Euclidean Geometry

Introduction to Non-Euclidean Geometry

  • Author: Harold E. Wolfe
  • Publisher: Courier Corporation
  • ISBN: 0486320375
  • Category: Mathematics
  • Page: 272
  • View: 9332
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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.

Challenging Problems in Geometry

Challenging Problems in Geometry

  • Author: Alfred S. Posamentier,Charles T. Salkind
  • Publisher: Courier Corporation
  • ISBN: 0486134865
  • Category: Mathematics
  • Page: 256
  • View: 3185
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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.

Geometry: Euclid and Beyond

Geometry: Euclid and Beyond

  • Author: Robin Hartshorne
  • Publisher: Springer Science & Business Media
  • ISBN: 0387226761
  • Category: Mathematics
  • Page: 528
  • View: 1870
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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.

Geometry by Construction

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: 6137
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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.

Problem-Solving Strategies

Problem-Solving Strategies

  • Author: Arthur Engel
  • Publisher: Springer Science & Business Media
  • ISBN: 0387226419
  • Category: Mathematics
  • Page: 403
  • View: 551
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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.

Euclidean Geometry

Euclidean Geometry

A First Course

  • Author: Mark Solomonovich
  • Publisher: iUniverse
  • ISBN: 1440153485
  • Category: Education
  • Page: 408
  • View: 6944
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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.

Philosophy of Mathematics and Deductive Structure in Euclid's Elements

Philosophy of Mathematics and Deductive Structure in Euclid's Elements

  • Author: Ian Mueller
  • Publisher: Courier Corporation
  • ISBN: 0486150879
  • Category: Mathematics
  • Page: 400
  • View: 3926
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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.

Lessons in Geometry: Plane geometry

Lessons in Geometry: Plane geometry

  • Author: Jacques Hadamard
  • Publisher: American Mathematical Soc.
  • ISBN: 0821843672
  • Category: Mathematics
  • Page: 330
  • View: 4708
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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.

Solving Mathematical Problems

Solving Mathematical Problems

A Personal Perspective

  • Author: Terence Tao
  • Publisher: OUP Oxford
  • ISBN: 0199205612
  • Category: Mathematics
  • Page: 103
  • View: 9245
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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.