Problem-Solving and Selected Topics in Euclidean Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Problem-Solving and Selected Topics in Euclidean Geometry write by Sotirios E. Louridas. This book was released on 2014-07-08. Problem-Solving and Selected Topics in Euclidean Geometry available in PDF, EPUB and Kindle. "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.
Euclidean Geometry in Mathematical Olympiads
Euclidean Geometry in Mathematical Olympiads - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Euclidean Geometry in Mathematical Olympiads write by Evan Chen. This book was released on 2021-08-23. Euclidean Geometry in Mathematical Olympiads available in PDF, EPUB and Kindle. 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.
Geometric Transformations
Geometric Transformations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometric Transformations write by Răzvan Gelca. This book was released on 2022-02-16. Geometric Transformations available in PDF, EPUB and Kindle. This textbook teaches the transformations of plane Euclidean geometry through problems, offering a transformation-based perspective on problems that have appeared in recent years at mathematics competitions around the globe, as well as on some classical examples and theorems. It is based on the combined teaching experience of the authors (coaches of several Mathematical Olympiad teams in Brazil, Romania and the USA) and presents comprehensive theoretical discussions of isometries, homotheties and spiral similarities, and inversions, all illustrated by examples and followed by myriad problems left for the reader to solve. These problems were carefully selected and arranged to introduce students to the topics by gradually moving from basic to expert level. Most of them have appeared in competitions such as Mathematical Olympiads or in mathematical journals aimed at an audience interested in mathematics competitions, while some are fundamental facts of mathematics discussed in the framework of geometric transformations. The book offers a global view of the geometric content of today's mathematics competitions, bringing many new methods and ideas to the attention of the public. Talented high school and middle school students seeking to improve their problem-solving skills can benefit from this book, as well as high school and college instructors who want to add nonstandard questions to their courses. People who enjoy solving elementary math problems as a hobby will also enjoy this work.
Problem-Solving and Selected Topics in Number Theory
Problem-Solving and Selected Topics in Number Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Problem-Solving and Selected Topics in Number Theory write by Michael Th. Rassias. This book was released on 2010-11-16. Problem-Solving and Selected Topics in Number Theory available in PDF, EPUB and Kindle. The book provides a self-contained introduction to classical Number Theory. All the proofs of the individual theorems and the solutions of the exercises are being presented step by step. Some historical remarks are also presented. The book will be directed to advanced undergraduate, beginning graduate students as well as to students who prepare for mathematical competitions (ex. Mathematical Olympiads and Putnam Mathematical competition).
Challenging Problems in Geometry
Challenging Problems in Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Challenging Problems in Geometry write by Alfred S. Posamentier. This book was released on 2012-04-30. Challenging Problems in Geometry available in PDF, EPUB and Kindle. 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.
