Basic Lessons On Isometries Similarities And Inversions In The Euclidean Plane A Synthetic Approach
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Basic Lessons On Isometries Similarities And Inversions In The Euclidean Plane
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Author : Ioannis Markos Roussos
language : en
Publisher: World Scientific
Release Date :
Basic Lessons On Isometries Similarities And Inversions In The Euclidean Plane written by Ioannis Markos Roussos and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Basic Lessons On Isometries Similarities And Inversions In The Euclidean Plane A Synthetic Approach
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Author : Ioannis Markos Roussos
language : en
Publisher: World Scientific
Release Date : 2021-09-03
Basic Lessons On Isometries Similarities And Inversions In The Euclidean Plane A Synthetic Approach written by Ioannis Markos Roussos and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-03 with Mathematics categories.
The aim of this book is to provide a complete synthetic exposition of plane isometries, similarities and inversions to readers who are interested in studying, teaching, and using this material.The topics developed in this book can provide new proofs and solutions to many results and problems of classical geometry, which are presented with different proofs in the literature. Their applications are numerous and some, such as the Steiner Chains and Point, are useful to engineers.The book contains many good examples, important applications and numerous exercises of various level and difficulty, which are classified in the three groups of: general exercises, geometrical constructions, and geometrical loci. Some lengthy exercises or groups of related exercises can be viewed as projects. On the basis of the above, this book, besides Classical Geometry, is an important addition to Mathematics Education.
Geometric Transformations
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Author : Răzvan Gelca
language : en
Publisher: Springer Nature
Release Date : 2022-02-16
Geometric Transformations written by Răzvan Gelca and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-16 with Mathematics categories.
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.
Geometry Illuminated
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Author : Matthew Harvey
language : en
Publisher: The Mathematical Association of America
Release Date : 2015-09-25
Geometry Illuminated written by Matthew Harvey and has been published by The Mathematical Association of America this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-25 with Mathematics categories.
Geometry Illuminated is an introduction to geometry in the plane, both Euclidean and hyperbolic. It is designed to be used in an undergraduate course on geometry, and as such, its target audience is undergraduate math majors. However, much of it should be readable by anyone who is comfortable with the language of mathematical proof. Throughout, the goal is to develop the material patiently. One of the more appealing aspects of geometry is that it is a very "visual" subject. This book hopes to takes full advantage of that, with an extensive use of illustrations as guides. Geometry Illuminated is divided into four principal parts. Part 1 develops neutral geometry in the style of Hilbert, including a discussion of the construction of measure in that system, ultimately building up to the Saccheri-Legendre Theorem. Part 2 provides a glimpse of classical Euclidean geometry, with an emphasis on concurrence results, such as the nine-point circle. Part 3 studies transformations of the Euclidean plane, beginning with isometries and ending with inversion, with applications and a discussion of area in between. Part 4 is dedicated to the development of the Poincaré disk model, and the study of geometry within that model. While this material is traditional, Geometry Illuminated does bring together topics that are generally not found in a book at this level. Most notably, it explicitly computes parametric equations for the pseudosphere and its geodesics. It focuses less on the nature of axiomatic systems for geometry, but emphasizes rather the logical development of geometry within such a system. It also includes sections dealing with trilinear and barycentric coordinates, theorems that can be proved using inversion, and Euclidean and hyperbolic tilings.
Transformation Geometry
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Author : Jagat Narain Kapur
language : en
Publisher:
Release Date : 1976
Transformation Geometry written by Jagat Narain Kapur and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Geometry, Algebraic categories.
Euclidean Geometry In Mathematical Olympiads
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Author : Evan Chen
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-08-23
Euclidean Geometry In Mathematical Olympiads written by Evan Chen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-23 with Education categories.
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.
Flavors Of Geometry
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Author : Silvio Levy
language : en
Publisher: Cambridge University Press
Release Date : 1997-09-28
Flavors Of Geometry written by Silvio Levy and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-09-28 with Mathematics categories.
Flavors of Geometry is a volume of lectures on four geometrically-influenced fields of mathematics that have experienced great development in recent years. Growing out of a series of introductory lectures given at the Mathematical Sciences Research Institute in January 1995 and January 1996, the book presents chapters by masters in their respective fields on hyperbolic geometry, dynamics in several complex variables, convex geometry, and volume estimation. Each lecture begins with a discussion of elementary concepts, examines the highlights of the field, and concludes with a look at more advanced material. The style and presentation of the chapters are clear and accessible, and most of the lectures are richly illustrated. Bibiliographies and indexes are included to encourage further reading on the topics discussed.
Geometry Of Surfaces
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Author : John Stillwell
language : en
Publisher: Springer Science & Business Media
Release Date : 1995-02-03
Geometry Of Surfaces written by John Stillwell and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-02-03 with Mathematics categories.
The geometry of surfaces is an ideal starting point for learning geometry, for, among other reasons, the theory of surfaces of constant curvature has maximal connectivity with the rest of mathematics. This text provides the student with the knowledge of a geometry of greater scope than the classical geometry taught today, which is no longer an adequate basis for mathematics or physics, both of which are becoming increasingly geometric. It includes exercises and informal discussions.
Discovering Geometry
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Author : Michael Serra
language : en
Publisher:
Release Date : 2003-03-01
Discovering Geometry written by Michael Serra and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-03-01 with Mathematics categories.
College Geometry
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Author : Howard Whitley Eves
language : en
Publisher: Jones & Bartlett Learning
Release Date : 1995
College Geometry written by Howard Whitley Eves and has been published by Jones & Bartlett Learning this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Computers categories.
College Geometry is divided into two parts. Part I is a sequel to basic high school geometry and introduces the reader to some of the important modern extensions of elementary geometry- extension that have largely entered into the mainstream of mathematics. Part II treats notions of geometric structure that arose with the non-Euclidean revolution in the first half of the nineteenth century.