Geometry in Problems

Häftad, Engelska, 2016

Del i serien MSRI Mathematical Circles Library

401 kr

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Beskrivning

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circles, and inscribed angles, remains an excellent playground for high-school mathematics students, even if it looks outdated from the professional mathematician's viewpoint.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

Produktinformation

Utgivningsdatum:2016-06-30
Mått:178 x 254 x undefined mm
Vikt:414 g
Format:Häftad
Språk:Engelska
Serie:MSRI Mathematical Circles Library
Antal sidor:214
Förlag:American Mathematical Society
ISBN:9781470419219

Utforska kategorier

Matematik inom Naturvetenskap och teknik

Mer om författaren

Alexander Shen, Institute of Problems of Information Transmission, Moscow, Russia, and LIRMM CNRS, Universite de Montpellier, France.

Recensioner i media

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

Innehållsförteckning

Measuring line segmentsMeasuring anglesThe triangle inequalityCongruent figuresTriangle congruence testsIsosceles trianglesCircleStraightedge and compass constructionsParallel linesRight trianglesParallelogramsRectangle, rhombus, squareGraph paperEquilateral trianglesMidsegment of a triangleIntercept theoremTrapezoidSimple inequalitiesReflection symmetryCentral symmetryAngles in a circleTangentsTwo circlesCircumscribed circle and perpendicular bisectorsInscribed circle (incircle)BisectorsInscribed and circumscribed quadrilateralsAreaThe Pythagorean TheoremSimilarityCoordinates on a lineCoordinates on a planeCommon measureTrigonometryAfterword