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Geometry in Problems

Alexander Shen Institute of Problems of Information Transmission, Moscow, Russia and LIRMM CNRS, Université de Montpellier, Montpellier, France
Translated from Russian by Marie Brodsky with assistance from Gina Yatsenko, Ray Droujkov, and Artem Astapchuk.
A co-publication of the AMS and Mathematical Sciences Research Institute
Available Formats:
Softcover ISBN: 978-1-4704-1921-9
Product Code: MCL/18
List Price: $25.00 Individual Price:$18.75
Electronic ISBN: 978-1-4704-3011-5
Product Code: MCL/18.E
List Price: $25.00 Individual Price:$18.75
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List Price: $37.50 Click above image for expanded view Geometry in Problems Alexander Shen Institute of Problems of Information Transmission, Moscow, Russia and LIRMM CNRS, Université de Montpellier, Montpellier, France Translated from Russian by Marie Brodsky with assistance from Gina Yatsenko, Ray Droujkov, and Artem Astapchuk. A co-publication of the AMS and Mathematical Sciences Research Institute Available Formats:  Softcover ISBN: 978-1-4704-1921-9 Product Code: MCL/18  List Price:$25.00 Individual Price: $18.75  Electronic ISBN: 978-1-4704-3011-5 Product Code: MCL/18.E  List Price:$25.00 Individual Price: $18.75 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$37.50
• Book Details

MSRI Mathematical Circles Library
Volume: 182016; 214 pp
MSC: Primary 51;

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circles, and inscribed angles, remains an excellent playground for high-school mathematics students, even if it looks outdated from the professional mathematician's viewpoint.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

Students, teachers, math circles organizers, parents, and others interested in teaching and learning basic plane geometry.

• Chapters
• Measuring line segments
• Measuring angles
• The triangle inequality
• Congruent figures
• Triangle congruence tests
• Isosceles triangles
• Circle
• Straightedge and compass constructions
• Parallel lines
• Right triangles
• Parallelograms
• Rectangle, rhombus, square
• Graph paper
• Equilateral triangles
• Midsegment of a triangle
• Intercept theorem
• Trapezoid
• Simple inequalities
• Reflection symmetry
• Central symmetry
• Angles in a circle
• Tangents
• Two circles
• Circumscribed circle and perpendicular bisectors
• Inscribed circle (incircle). Bisectors
• Area
• The Pythagorean Theorem
• Similarity
• Coordinates on a line
• Coordinates on a plane
• Common measure
• Trigonometry
• Afterword

• Requests

Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
Volume: 182016; 214 pp
MSC: Primary 51;

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

Students, teachers, math circles organizers, parents, and others interested in teaching and learning basic plane geometry.

• Chapters
• Measuring line segments
• Measuring angles
• The triangle inequality
• Congruent figures
• Triangle congruence tests
• Isosceles triangles
• Circle
• Straightedge and compass constructions
• Parallel lines
• Right triangles
• Parallelograms
• Rectangle, rhombus, square
• Graph paper
• Equilateral triangles
• Midsegment of a triangle
• Intercept theorem
• Trapezoid
• Simple inequalities
• Reflection symmetry
• Central symmetry
• Angles in a circle
• Tangents
• Two circles
• Circumscribed circle and perpendicular bisectors
• Inscribed circle (incircle). Bisectors