Methods Of Solving Complex Geometry Problems
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Methods Of Solving Complex Geometry Problems
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Author : Ellina Grigorieva
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-08-13
Methods Of Solving Complex Geometry Problems written by Ellina Grigorieva 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 2013-08-13 with Mathematics categories.
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.
Challenging Problems In Geometry
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Author : Alfred S. Posamentier
language : en
Publisher: Courier Corporation
Release Date : 2012-04-30
Challenging Problems In Geometry written by Alfred S. Posamentier and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-30 with Mathematics categories.
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.
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.
Methods Of Solving Nonstandard Problems
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Author : Ellina Grigorieva
language : en
Publisher: Birkhäuser
Release Date : 2015-09-17
Methods Of Solving Nonstandard Problems written by Ellina Grigorieva and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-17 with Mathematics categories.
This book, written by an accomplished female mathematician, is the second to explore nonstandard mathematical problems – those that are not directly solved by standard mathematical methods but instead rely on insight and the synthesis of a variety of mathematical ideas. It promotes mental activity as well as greater mathematical skills, and is an ideal resource for successful preparation for the mathematics Olympiad. Numerous strategies and techniques are presented that can be used to solve intriguing and challenging problems of the type often found in competitions. The author uses a friendly, non-intimidating approach to emphasize connections between different fields of mathematics and often proposes several different ways to attack the same problem. Topics covered include functions and their properties, polynomials, trigonometric and transcendental equations and inequalities, optimization, differential equations, nonlinear systems, and word problems. Over 360 problems are included with hints, answers, and detailed solutions. Methods of Solving Nonstandard Problems will interest high school and college students, whether they are preparing for a math competition or looking to improve their mathematical skills, as well as anyone who enjoys an intellectual challenge and has a special love for mathematics. Teachers and college professors will be able to use it as an extra resource in the classroom to augment a conventional course of instruction in order to stimulate abstract thinking and inspire original thought.
Methods Of Solving Sequence And Series Problems
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Author : Ellina Grigorieva
language : en
Publisher: Birkhäuser
Release Date : 2016-12-09
Methods Of Solving Sequence And Series Problems written by Ellina Grigorieva and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-09 with Mathematics categories.
This book aims to dispel the mystery and fear experienced by students surrounding sequences, series, convergence, and their applications. The author, an accomplished female mathematician, achieves this by taking a problem solving approach, starting with fascinating problems and solving them step by step with clear explanations and illuminating diagrams. The reader will find the problems interesting, unusual, and fun, yet solved with the rigor expected in a competition. Some problems are taken directly from mathematics competitions, with the name and year of the exam provided for reference. Proof techniques are emphasized, with a variety of methods presented. The text aims to expand the mind of the reader by often presenting multiple ways to attack the same problem, as well as drawing connections with different fields of mathematics. Intuitive and visual arguments are presented alongside technical proofs to provide a well-rounded methodology. With nearly 300 problems including hints, answers, and solutions, Methods of Solving Sequences and Series Problems is an ideal resource for those learning calculus, preparing for mathematics competitions, or just looking for a worthwhile challenge. It can also be used by faculty who are looking for interesting and insightful problems that are not commonly found in other textbooks.
Complex Numbers From A To Z
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Author : Titu Andreescu
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-10-08
Complex Numbers From A To Z written by Titu Andreescu 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 2007-10-08 with Mathematics categories.
* Learn how complex numbers may be used to solve algebraic equations, as well as their geometric interpretation * Theoretical aspects are augmented with rich exercises and problems at various levels of difficulty * A special feature is a selection of outstanding Olympiad problems solved by employing the methods presented * May serve as an engaging supplemental text for an introductory undergrad course on complex numbers or number theory
Methods For Solving Complex Problems In Fluids Engineering
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Author : Can Kang
language : en
Publisher: Springer
Release Date : 2019-01-12
Methods For Solving Complex Problems In Fluids Engineering written by Can Kang and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-12 with Technology & Engineering categories.
This book describes recently developed research methods used to study complex problems in fluid engineering, especially optical flow measurement, flow visualization and numerical methods. It includes a wealth of diagrams and images, and the content is presented in a step-by-step manner from beginning to end, helping readers grasp the central points of the book. The book also presents a number of practical cases, illustrating how the research methods covered can be concretely implemented. Lastly, the book offers a valuable point of departure for pursuing further research.
Meshless Methods And Their Numerical Properties
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Author : Hua Li
language : en
Publisher: CRC Press
Release Date : 2013-02-22
Meshless Methods And Their Numerical Properties written by Hua Li and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-22 with Mathematics categories.
Meshless, or meshfree methods, which overcome many of the limitations of the finite element method, have achieved significant progress in numerical computations of a wide range of engineering problems. A comprehensive introduction to meshless methods, Meshless Methods and Their Numerical Properties gives complete mathematical formulations for the most important and classical methods, as well as several methods recently developed by the authors. This book also offers a rigorous mathematical treatment of their numerical properties—including consistency, convergence, stability, and adaptivity—to help you choose the method that is best suited for your needs. Get Guidance for Developing and Testing Meshless Methods Developing a broad framework to study the numerical computational characteristics of meshless methods, the book presents consistency, convergence, stability, and adaptive analyses to offer guidance for developing and testing a particular meshless method. The authors demonstrate the numerical properties by solving several differential equations, which offer a clearer understanding of the concepts. They also explain the difference between the finite element and meshless methods. Explore Engineering Applications of Meshless Methods The book examines how meshless methods can be used to solve complex engineering problems with lower computational cost, higher accuracy, easier construction of higher-order shape functions, and easier handling of large deformation and nonlinear problems. The numerical examples include engineering problems such as the CAD design of MEMS devices, nonlinear fluid-structure analysis of near-bed submarine pipelines, and two-dimensional multiphysics simulation of pH-sensitive hydrogels. Appendices supply useful template functions, flowcharts, and data structures to assist you in implementing meshless methods. Choose the Best Method for a Particular Problem Providing insight into the special features and intricacies of meshless methods, this is a valuable reference for anyone developing new high-performance numerical methods or working on the modelling and simulation of practical engineering problems. It guides you in comparing and verifying meshless methods so that you can more confidently select the best method to solve a particular problem.
Methods For Euclidean Geometry
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Author : Owen Byer
language : en
Publisher: American Mathematical Soc.
Release Date : 2010-12-31
Methods For Euclidean Geometry written by Owen Byer 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 2010-12-31 with Mathematics categories.
Euclidean plane geometry is one of the oldest and most beautiful topics in mathematics. Instead of carefully building geometries from axiom sets, this book uses a wealth of methods to solve problems in Euclidean geometry. Many of these methods arose where existing techniques proved inadequate. In several cases, the new ideas used in solving specific problems later developed into independent areas of mathematics. This book is primarily a geometry textbook, but studying geometry in this way will also develop students' appreciation of the subject and of mathematics as a whole. For instance, despite the fact that the analytic method has been part of mathematics for four centuries, it is rarely a tool a student considers using when faced with a geometry problem. Methods for Euclidean Geometry explores the application of a broad range of mathematical topics to the solution of Euclidean problems.
Multivariate Calculus And Geometry Concepts
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Author : Chirag Verma
language : en
Publisher: Educohack Press
Release Date : 2025-02-20
Multivariate Calculus And Geometry Concepts written by Chirag Verma and has been published by Educohack Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-20 with Science categories.
"Multivariate Calculus and Geometry Concepts" is a comprehensive textbook designed to provide students, researchers, and practitioners with a thorough understanding of fundamental concepts, techniques, and applications in multivariate calculus and geometry. Authored by experts, we offer a balanced blend of theoretical foundations, practical examples, and computational methods, making it suitable for both classroom instruction and self-study. We cover a wide range of topics, including partial derivatives, gradients, line and surface integrals, parametric equations, polar coordinates, conic sections, and differential forms. Each topic is presented clearly and concisely, with detailed explanations and illustrative examples to aid understanding. Our emphasis is on developing a conceptual understanding of key concepts and techniques, rather than rote memorization of formulas. We include numerous figures, diagrams, and geometric interpretations to help readers visualize abstract mathematical concepts and their real-world applications. Practical applications of multivariate calculus and geometry are highlighted throughout the book, with examples drawn from physics, engineering, computer graphics, and other fields. We demonstrate how these concepts are used to solve real-world problems and inspire readers to apply their knowledge in diverse areas. We discuss computational methods and numerical techniques used in multivariate calculus and geometry, such as numerical integration, optimization algorithms, and finite element methods. Programming exercises and computer simulations provide hands-on experience with implementing and applying these methods. Our supplementary resources include online tutorials, solution manuals, and interactive simulations, offering additional guidance, practice problems, and opportunities for further exploration and self-assessment. "Multivariate Calculus and Geometry Concepts" is suitable for undergraduate and graduate students in mathematics, engineering, physics, computer science, and related disciplines. It also serves as a valuable reference for researchers, educators, and professionals seeking a comprehensive overview of multivariate calculus and geometry and its applications in modern science and technology.