Challenges in Geometry

Challenges in Geometry

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  • Author: Christopher J. Bradley
  • Publisher: Oxford University Press on Demand
  • ISBN: 0198566913
  • Category : Mathematics
  • Languages : en
  • Pages : 218

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.


Challenging Problems in Geometry

Challenging Problems in Geometry

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  • Author: Alfred S. Posamentier
  • Publisher: Courier Corporation
  • ISBN: 0486134865
  • Category : Mathematics
  • Languages : en
  • Pages : 275

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 in Problems

Geometry in Problems

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  • Author: Alexander Shen
  • Publisher: American Mathematical Soc.
  • ISBN: 1470419211
  • Category : Geometry
  • Languages : en
  • Pages : 214

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circles, and inscribed angles, remains an excellent playground for high-school mathematics students, even if it looks outdated from the professional mathematician's viewpoint.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


The Humongous Book of Geometry Problems

The Humongous Book of Geometry Problems

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  • Author: W. Michael Kelley
  • Publisher: Penguin
  • ISBN: 1615646981
  • Category : Mathematics
  • Languages : en
  • Pages : 594

An ingenious problem-solving solution for befuddled math students. A bestselling math book author takes what appears to be a typical geometry workbook, full of solved problems, and makes notes in the margins adding missing steps and simplifying concepts so that otherwise baffling solutions are made perfectly clear. By learning how to interpret and solve problems as they are presented in courses, students become fully prepared to solve any obscure problem. No more solving by trial and error! - Includes 1000 problems and solutions - Annotations throughout the text clarify each problem and fill in missing steps needed to reach the solution, making this book like no other geometry workbook on the market - The previous two books in the series on calculus and algebra sell very well


Methods of Solving Complex Geometry Problems

Methods of Solving Complex Geometry Problems

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  • Author: Ellina Grigorieva
  • Publisher: Springer Science & Business Media
  • ISBN: 331900705X
  • Category : Mathematics
  • Languages : en
  • Pages : 234

This book is a unique collection of challenging geometry problems and detailed solutions that will build students’ confidence in mathematics. By proposing several methods to approach each problem and emphasizing geometry’s connections with different fields of mathematics, Methods of Solving Complex Geometry Problems serves as a bridge to more advanced problem solving. Written by an accomplished female mathematician who struggled with geometry as a child, it does not intimidate, but instead fosters the reader’s ability to solve math problems through the direct application of theorems. Containing over 160 complex problems with hints and detailed solutions, Methods of Solving Complex Geometry Problems can be used as a self-study guide for mathematics competitions and for improving problem-solving skills in courses on plane geometry or the history of mathematics. It contains important and sometimes overlooked topics on triangles, quadrilaterals, and circles such as the Menelaus-Ceva theorem, Simson’s line, Heron’s formula, and the theorems of the three altitudes and medians. It can also be used by professors as a resource to stimulate the abstract thinking required to transcend the tedious and routine, bringing forth the original thought of which their students are capable. Methods of Solving Complex Geometry Problems will interest high school and college students needing to prepare for exams and competitions, as well as anyone who enjoys an intellectual challenge and has a special love of geometry. It will also appeal to instructors of geometry, history of mathematics, and math education courses.


Challenges in Geometry

Challenges in Geometry

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  • Author:
  • Publisher:
  • ISBN:
  • Category :
  • Languages : en
  • Pages : 205


Compiled and Solved Problems in Geometry and Trigonometry

Compiled and Solved Problems in Geometry and Trigonometry

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  • Author: Florentin Smarandache
  • Publisher: Infinite Study
  • ISBN: 1599732998
  • Category : Geometry
  • Languages : en
  • Pages : 221

This book is a translation from Romanian of "Probleme Compilate şi Rezolvate de Geometrie şi Trigonometrie" (University of Kishinev Press, Kishinev, 169 p., 1998), and includes problems of 2D and 3D Euclidean geometry plus trigonometry, compiled and solved from the Romanian Textbooks for 9th and 10th grade students.


Solving Problems in Geometry

Solving Problems in Geometry

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  • Author: Kim Hoo Hang
  • Publisher: World Scientific Publishing Company
  • ISBN: 9814583766
  • Category :
  • Languages : en
  • Pages : 356

This new volume of the Mathematical Olympiad Series focuses on the topic of geometry. Basic and advanced theorems commonly seen in Mathematical Olympiad are introduced and illustrated with plenty of examples. Special techniques in solving various types of geometrical problems are also introduced, while the authors elaborate extensively on how to acquire an insight and develop strategies in tackling difficult geometrical problems. This book is suitable for any reader with elementary geometrical knowledge at the lower secondary level. Each chapter includes sufficient scaffolding and is comprehensive enough for the purpose of self-study. Readers who complete the chapters on the basic theorems and techniques would acquire a good foundation in geometry and may attempt to solve many geometrical problems in various mathematical competitions. Meanwhile, experienced contestants in Mathematical Olympiad competitions will find a large collection of problems pitched at competitions at the international level, with opportunities to practise and sharpen their problem-solving skills in geometry. Request Inspection Copy


Geometry's Oldest Challenges

Geometry's Oldest Challenges

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  • Author: Antonio Pedagno
  • Publisher:
  • ISBN: 9780806227795
  • Category : Geometry
  • Languages : en
  • Pages : 60


107 Geometry Problems from the AwesomeMath Year-round Program

107 Geometry Problems from the AwesomeMath Year-round Program

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  • Author: Titu Andreescu
  • Publisher:
  • ISBN: 9780979926976
  • Category : Geometry
  • Languages : en
  • Pages : 0

This book contains 107 geometry problems used in the AwesomeMath Year-Round Program. The problems offer additional challenges for those who have progressed through the 106 Geometry Problems from the AwesomeMath Summer Camp publication. The book begins with a theoretical chapter, where the authors review basic facts and familiarize the reader with some more advanced techniques. The authors then proceed to the main part of the work, the problem sections. The problems are a carefully selected and balanced mix which offers a vast variety of flavors and difficulties, ranging from AMC and AIME levels to high-end IMO problems. Out of thousands of Olympiad problems from around the globe the authors chose those which best illustrate the featured techniques and their applications. The problems meet the authors' demanding taste and fully exhibit the enchanting beauty of classical geometry. For every problem the authors provide a detailed solution and strive to pass on the intuition and motivation behind it. Numerous problems have multiple solutions.Directly experiencing Olympiad geometry both as contestants and instructors, the authors are convinced that a neat diagram is essential to efficiently solve a geometry problem. Their diagrams do not contain anything superfluous, yet emphasize the key elements and benefit from a good choice of orientation. Many of the proofs should be legible only from looking at the diagrams.