Euclidean Geometry In Mathematical Olympiads

Author : Evan Chen
Publisher : American Mathematical Soc.
ISBN 13 : 1470466201
Total Pages : 311 pages
Book Rating : 4.06/5 ( download)

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Download or read book Euclidean Geometry in Mathematical Olympiads written by Evan Chen and published by American Mathematical Soc.. This book was released on 2021-08-23 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Evan Chen
Publisher : The Mathematical Association of America
ISBN 13 : 0883858398
Total Pages : 329 pages
Book Rating : 4.94/5 ( download)

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Download or read book Euclidean Geometry in Mathematical Olympiads written by Evan Chen and published by The Mathematical Association of America. This book was released on 2016-05-02 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 as 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 : Evan Chen (Mathematician)
Publisher :
ISBN 13 : 9781614444114
Total Pages : 311 pages
Book Rating : 4.10/5 ( download)

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Download or read book Euclidean Geometry in Mathematical Olympiads written by Evan Chen (Mathematician) and published by . This book was released on 2016 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Sotirios E. Louridas
Publisher : Springer Science & Business Media
ISBN 13 : 1461472733
Total Pages : 235 pages
Book Rating : 4.35/5 ( download)

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Download or read book Problem-Solving and Selected Topics in Euclidean Geometry written by Sotirios E. Louridas and published by Springer Science & Business Media. This book was released on 2014-07-08 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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.

Author : Roger A. Johnson
Publisher : Courier Corporation
ISBN 13 : 048615498X
Total Pages : 338 pages
Book Rating : 4.85/5 ( download)

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Download or read book Advanced Euclidean Geometry written by Roger A. Johnson and published by Courier Corporation. This book was released on 2013-01-08 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : M. N. Aref
Publisher : Courier Corporation
ISBN 13 : 0486477207
Total Pages : 274 pages
Book Rating : 4.06/5 ( download)

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Download or read book Problems and Solutions in Euclidean Geometry written by M. N. Aref and published by Courier Corporation. This book was released on 2010-01-01 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Christopher J. Bradley
Publisher : Oxford University Press on Demand
ISBN 13 : 0198566913
Total Pages : 218 pages
Book Rating : 4.15/5 ( download)

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Download or read book Challenges in Geometry written by Christopher J. Bradley and published by Oxford University Press on Demand. This book was released on 2005-02-17 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: Containing numerous exercises, illustrations, hints and solutions, presented in a lucid and thought-provoking style, this text provides a wide range of skills required in competitions such as the Mathematical Olympiad. With more than fifty problems in Euclidean geometry, it is ideal for Mathematical Olympiad training and also serves as a supplementary text for students in pure mathematics, particularly number theory and geometry.

Author : H. S. M. Coxeter
Publisher : American Mathematical Society
ISBN 13 : 1470466414
Total Pages : 193 pages
Book Rating : 4.11/5 ( download)

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Download or read book Geometry Revisited written by H. S. M. Coxeter and published by American Mathematical Society. This book was released on 2021-12-30 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: Among the many beautiful and nontrivial theorems in geometry found in Geometry Revisited are the theorems of Ceva, Menelaus, Pappus, Desargues, Pascal, and Brianchon. A nice proof is given of Morley's remarkable theorem on angle trisectors. The transformational point of view is emphasized: reflections, rotations, translations, similarities, inversions, and affine and projective transformations. Many fascinating properties of circles, triangles, quadrilaterals, and conics are developed.

Author : Titu Andreescu
Publisher :
ISBN 13 : 9780988562233
Total Pages : 0 pages
Book Rating : 4.35/5 ( download)

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Download or read book Lemmas in Olympiad Geometry written by Titu Andreescu and published by . This book was released on 2016 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book showcases the synthetic problem-solving methods which frequently appear in modern day Olympiad geometry, in the way we believe they should be taught to someone with little familiarity in the subject. In some sense, the text also represents an unofficial sequel to the recent problem collection published by XYZ Press, 110 Geometry Problems for the International Mathematical Olympiad, written by the first and third authors, but the two books can be studied completely independently of each other. The work is designed as a medley of the important Lemmas in classical geometry in a relatively linear fashion: gradually starting from Power of a Point and common results to more sophisticated topics, where knowing a lot of techniques can prove to be tremendously useful. We treat each chapter as a short story of its own and include numerous solved exercises with detailed explanations and related insights that will hopefully make your journey very enjoyable.

Author : D. O. Shklarsky
Publisher : Courier Corporation
ISBN 13 : 0486319865
Total Pages : 480 pages
Book Rating : 4.65/5 ( download)

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Download or read book The USSR Olympiad Problem Book written by D. O. Shklarsky and published by Courier Corporation. This book was released on 2013-04-15 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over 300 challenging problems in algebra, arithmetic, elementary number theory and trigonometry, selected from Mathematical Olympiads held at Moscow University. Only high school math needed. Includes complete solutions. Features 27 black-and-white illustrations. 1962 edition.