Euclidean Geometry In Mathematical Olympiads

Author : Evan Chen
Publisher : American Mathematical Soc.
Page : 311 pages
File Size : 50,5 Mb
Release : 2021-08-23
Category : Education
ISBN : 9781470466206

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Euclidean Geometry in Mathematical Olympiads by Evan Chen Pdf

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
Page : 329 pages
File Size : 53,8 Mb
Release : 2016-05-02
Category : Mathematics
ISBN : 9780883858394

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Euclidean Geometry in Mathematical Olympiads by Evan Chen Pdf

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 : Unknown
Page : 311 pages
File Size : 43,9 Mb
Release : 2016
Category : Geometry
ISBN : 1614444110

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Euclidean Geometry in Mathematical Olympiads by Evan Chen (Mathematician) Pdf

Author : Sotirios E. Louridas,Michael Th. Rassias
Publisher : Springer Science & Business Media
Page : 235 pages
File Size : 46,6 Mb
Release : 2014-07-08
Category : Mathematics
ISBN : 9781461472735

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Problem-Solving and Selected Topics in Euclidean Geometry by Sotirios E. Louridas,Michael Th. Rassias Pdf

"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 : George Polya,Jeremy Kilpatrick
Publisher : Courier Corporation
Page : 80 pages
File Size : 46,7 Mb
Release : 2013-04-09
Category : Mathematics
ISBN : 9780486318325

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The Stanford Mathematics Problem Book by George Polya,Jeremy Kilpatrick Pdf

Based on Stanford University's well-known competitive exam, this excellent mathematics workbook offers students at both high school and college levels a complete set of problems, hints, and solutions. 1974 edition.

Author : Robin Hartshorne
Publisher : Springer Science & Business Media
Page : 535 pages
File Size : 49,6 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9780387226767

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Geometry: Euclid and Beyond by Robin Hartshorne Pdf

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.

Author : Christopher J. Bradley
Publisher : Oxford University Press on Demand
Page : 218 pages
File Size : 47,5 Mb
Release : 2005-02-17
Category : Mathematics
ISBN : 9780198566915

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Challenges in Geometry by Christopher J. Bradley Pdf

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 : Jack Noah
Publisher : Createspace Independent Publishing Platform
Page : 318 pages
File Size : 51,9 Mb
Release : 2017-06-07
Category : Electronic
ISBN : 1548061700

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Euclidean Geometry in Mathematical Olympiads by Jack Noah Pdf

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.

Author : M. N. Aref,William Wernick
Publisher : Courier Corporation
Page : 274 pages
File Size : 44,9 Mb
Release : 2010-01-01
Category : Mathematics
ISBN : 9780486477206

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Problems and Solutions in Euclidean Geometry by M. N. Aref,William Wernick Pdf

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 : H. S. M. Coxeter,S. L. Greitzer
Publisher : American Mathematical Society
Page : 193 pages
File Size : 44,8 Mb
Release : 2021-12-30
Category : Mathematics
ISBN : 9781470466411

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Geometry Revisited by H. S. M. Coxeter,S. L. Greitzer Pdf

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,Sam Korsky,Cosmin Pohoata
Publisher : Unknown
Page : 0 pages
File Size : 42,5 Mb
Release : 2016
Category : Geometry
ISBN : 0988562235

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Lemmas in Olympiad Geometry by Titu Andreescu,Sam Korsky,Cosmin Pohoata Pdf

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 : David J. Morin
Publisher : Createspace Independent Publishing Platform
Page : 0 pages
File Size : 46,8 Mb
Release : 2014
Category : Mechanics
ISBN : 1482086921

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Problems and Solutions in Introductory Mechanics by David J. Morin Pdf

This problem book is ideal for high-school and college students in search of practice problems with detailed solutions. All of the standard introductory topics in mechanics are covered: kinematics, Newton's laws, energy, momentum, angular momentum, oscillations, gravity, and fictitious forces. The introduction to each chapter provides an overview of the relevant concepts. Students can then warm up with a series of multiple-choice questions before diving into the free-response problems which constitute the bulk of the book. The first few problems in each chapter are derivations of key results/theorems that are useful when solving other problems. While the book is calculus-based, it can also easily be used in algebra-based courses. The problems that require calculus (only a sixth of the total number) are listed in an appendix, allowing students to steer clear of those if they wish. Additional details: (1) Features 150 multiple-choice questions and nearly 250 free-response problems, all with detailed solutions. (2) Includes 350 figures to help students visualize important concepts. (3) Builds on solutions by frequently including extensions/variations and additional remarks. (4) Begins with a chapter devoted to problem-solving strategies in physics. (5) A valuable supplement to the assigned textbook in any introductory mechanics course.

Author : Terence Tao
Publisher : OUP Oxford
Page : 116 pages
File Size : 45,5 Mb
Release : 2006-07-28
Category : Mathematics
ISBN : 9780191568695

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Solving Mathematical Problems by Terence Tao Pdf

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 of 14 years and above in pure mathematics.

Author : Răzvan Gelca,Titu Andreescu
Publisher : Springer
Page : 857 pages
File Size : 48,8 Mb
Release : 2017-09-19
Category : Mathematics
ISBN : 9783319589886

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Putnam and Beyond by Răzvan Gelca,Titu Andreescu Pdf

This book takes the reader on a journey through the world of college mathematics, focusing on some of the most important concepts and results in the theories of polynomials, linear algebra, real analysis, differential equations, coordinate geometry, trigonometry, elementary number theory, combinatorics, and probability. Preliminary material provides an overview of common methods of proof: argument by contradiction, mathematical induction, pigeonhole principle, ordered sets, and invariants. Each chapter systematically presents a single subject within which problems are clustered in each section according to the specific topic. The exposition is driven by nearly 1300 problems and examples chosen from numerous sources from around the world; many original contributions come from the authors. The source, author, and historical background are cited whenever possible. Complete solutions to all problems are given at the end of the book. This second edition includes new sections on quad ratic polynomials, curves in the plane, quadratic fields, combinatorics of numbers, and graph theory, and added problems or theoretical expansion of sections on polynomials, matrices, abstract algebra, limits of sequences and functions, derivatives and their applications, Stokes' theorem, analytical geometry, combinatorial geometry, and counting strategies. Using the W.L. Putnam Mathematical Competition for undergraduates as an inspiring symbol to build an appropriate math background for graduate studies in pure or applied mathematics, the reader is eased into transitioning from problem-solving at the high school level to the university and beyond, that is, to mathematical research. This work may be used as a study guide for the Putnam exam, as a text for many different problem-solving courses, and as a source of problems for standard courses in undergraduate mathematics. Putnam and Beyond is organized for independent study by undergraduate and gradu ate students, as well as teachers and researchers in the physical sciences who wish to expand their mathematical horizons.

Author : Derek Holton
Publisher : World Scientific Publishing Company
Page : 292 pages
File Size : 51,7 Mb
Release : 2009-07-30
Category : Mathematics
ISBN : 9789814365253

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A First Step to Mathematical Olympiad Problems by Derek Holton Pdf

See also A SECOND STEP TO MATHEMATICAL OLYMPIAD PROBLEMS The International Mathematical Olympiad (IMO) is an annual international mathematics competition held for pre-collegiate students. It is also the oldest of the international science olympiads, and competition for places is particularly fierce. This book is an amalgamation of the first 8 of 15 booklets originally produced to guide students intending to contend for placement on their country's IMO team. The material contained in this book provides an introduction to the main mathematical topics covered in the IMO, which are: Combinatorics, Geometry and Number Theory. In addition, there is a special emphasis on how to approach unseen questions in Mathematics, and model the writing of proofs. Full answers are given to all questions. Though A First Step to Mathematical Olympiad Problems is written from the perspective of a mathematician, it is written in a way that makes it easily comprehensible to adolescents. This book is also a must-read for coaches and instructors of mathematical competitions.