Geometrical Kaleidoscope (Second Edition) PDF Download
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Author: Boris Pritsker
Publisher: World Scientific
ISBN: 9811285292
Category : Mathematics
Languages : en
Pages : 188
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Book Description
The goal of the book is to provide insight into many enjoyable and fascinating aspects of geometry, and to reveal interesting geometrical properties. The emphasis is on the practical applications of theory in the problem-solving process. The chapters cover a myriad of topics among which are the classic theorems and formulas such as Archimedes' Law of the Lever, the Pythagorean Theorem, Heron's formula, Brahmagupta's formula, Appollonius's Theorem, Euler's line properties, the Nine-Point Circle, Fagnano's Problem, the Steiner-Lehmus Theorem, Napoleon's Theorem, Ceva's Theorem, Menelaus's Theorem, Pompeiu's Theorem, and Morley's Miracle. The book focuses on geometric thinking — what it means, how to develop it, and how to recognize it. 'Geometrical Kaleidoscope' consists of a kaleidoscope of topics that seem to not be related at first glance. However, that perception disappears as you go from chapter to chapter and explore the multitude of surprising relationships, unexpected connections, and links. Readers solving a chain of problems will learn from them general techniques, rather than isolated instances of the application of a technique. In spite of the many problems' challenging character, their solutions require no more than a basic knowledge covered in a high school geometry curriculum. There are plenty of problems for readers to work out for themselves (solutions are provided at the end of the book).In the 2nd edition of the book there are many new ideas and additional explanations that help the reader better understand the solutions of problems and connect the chapters to one another. A new chapter 'Alternative proofs of the Pythagorean Theorem' is added. It covers seven different proofs of the famous theorem and discusses its generalizations and applications. There is also Appendix and Index added, which were missing in the first edition of the book.
Author: Boris Pritsker
Publisher: World Scientific
ISBN: 9811285292
Category : Mathematics
Languages : en
Pages : 188
Get Book Here
Book Description
The goal of the book is to provide insight into many enjoyable and fascinating aspects of geometry, and to reveal interesting geometrical properties. The emphasis is on the practical applications of theory in the problem-solving process. The chapters cover a myriad of topics among which are the classic theorems and formulas such as Archimedes' Law of the Lever, the Pythagorean Theorem, Heron's formula, Brahmagupta's formula, Appollonius's Theorem, Euler's line properties, the Nine-Point Circle, Fagnano's Problem, the Steiner-Lehmus Theorem, Napoleon's Theorem, Ceva's Theorem, Menelaus's Theorem, Pompeiu's Theorem, and Morley's Miracle. The book focuses on geometric thinking — what it means, how to develop it, and how to recognize it. 'Geometrical Kaleidoscope' consists of a kaleidoscope of topics that seem to not be related at first glance. However, that perception disappears as you go from chapter to chapter and explore the multitude of surprising relationships, unexpected connections, and links. Readers solving a chain of problems will learn from them general techniques, rather than isolated instances of the application of a technique. In spite of the many problems' challenging character, their solutions require no more than a basic knowledge covered in a high school geometry curriculum. There are plenty of problems for readers to work out for themselves (solutions are provided at the end of the book).In the 2nd edition of the book there are many new ideas and additional explanations that help the reader better understand the solutions of problems and connect the chapters to one another. A new chapter 'Alternative proofs of the Pythagorean Theorem' is added. It covers seven different proofs of the famous theorem and discusses its generalizations and applications. There is also Appendix and Index added, which were missing in the first edition of the book.
Author: Spyros Horemis
Publisher: Courier Corporation
ISBN: 0486201805
Category : Art
Languages : en
Pages : 50
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Book Description
Beautifully rendered, imaginative new geometrical designs. 46 designs.
Author: Boris Pritsker
Publisher: Courier Dover Publications
ISBN: 048684305X
Category : Mathematics
Languages : en
Pages : 337
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Book Description
Equations are the lifeblood of mathematics, science, and technology, and this book examines equations of all kinds. With his masterful ability to convey the excitement and elegance of mathematics, author Boris Pritsker explores equations from the simplest to the most complex—their history, their charm, and their usefulness in solving problems. The Equations World bridges the fields of algebra, geometry, number theory, and trigonometry, solving more than 280 problems by employing a wide spectrum of techniques. The author demystifies the subject with efficient hints, tricks, and methods that reveal the fun and satisfaction of problem solving. He also demonstrates how equations can serve as important tools for expressing a problem's data, showing the ways in which they assist in fitting parts together to solve the whole puzzle. In addition, brief historical tours reveal the foundations of mathematical thought by tracing the ideas and approaches developed by mathematicians over the centuries. Both recreational mathematicians and ambitious students will find this book an ample source of enlightenment and enjoyment.
Author: Boris Pritsker
Publisher: Courier Dover Publications
ISBN: 0486832805
Category : Mathematics
Languages : en
Pages : 337
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Book Description
Equations are the lifeblood of mathematics, science, and technology, and this book examines equations of all kinds. With his masterful ability to convey the excitement and elegance of mathematics, author Boris Pritsker explores equations from the simplest to the most complex—their history, their charm, and their usefulness in solving problems. The Equations World bridges the fields of algebra, geometry, number theory, and trigonometry, solving more than 280 problems by employing a wide spectrum of techniques. The author demystifies the subject with efficient hints, tricks, and methods that reveal the fun and satisfaction of problem solving. He also demonstrates how equations can serve as important tools for expressing a problem's data, showing the ways in which they assist in fitting parts together to solve the whole puzzle. In addition, brief historical tours reveal the foundations of mathematical thought by tracing the ideas and approaches developed by mathematicians over the centuries. Both recreational mathematicians and ambitious students will find this book an ample source of enlightenment and enjoyment.
Author: R. A. Peterson
Publisher:
ISBN:
Category : Geophysics
Languages : en
Pages : 188
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Book Description
Author: Friedrich Carl Ludwig SCHOEDLER
Publisher:
ISBN:
Category :
Languages : en
Pages : 646
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Book Description
Author: C. Mammana
Publisher: Springer Science & Business Media
ISBN: 9401152268
Category : Education
Languages : en
Pages : 353
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Book Description
In recent years geometry seems to have lost large parts of its former central position in mathematics teaching in most countries. However, new trends have begun to counteract this tendency. There is an increasing awareness that geometry plays a key role in mathematics and learning mathematics. Although geometry has been eclipsed in the mathematics curriculum, research in geometry has blossomed as new ideas have arisen from inside mathematics and other disciplines, including computer science. Due to reassessment of the role of geometry, mathematics educators and mathematicians face new challenges. In the present ICMI study, the whole spectrum of teaching and learning of geometry is analysed. Experts from all over the world took part in this study, which was conducted on the basis of recent international research, case studies, and reports on actual school practice. This book will be of particular interest to mathematics educators and mathematicians who are involved in the teaching of geometry at all educational levels, as well as to researchers in mathematics education.
Author: Stanislav Grof
Publisher: State University of New York Press
ISBN: 1438496435
Category : Psychology
Languages : en
Pages : 425
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Book Description
In the second edition of this classic text, Stanislav Grof and Christina Grof describe their groundbreaking form of self-exploration and psychotherapy: holotropic breathwork. Holotropic means "moving toward wholeness," from the Greek holos (whole) and trepein (moving in the direction of). The breathwork utilizes the remarkable healing and transformative potential of nonordinary states of consciousness. These states engender a rich array of experiences with unique healing potential—reliving childhood memories, infancy, birth and prenatal life, and elements from the historical and archetypal realms of the collective unconscious. Induced by very simple means—a combination of accelerated breathing, evocative music, and bodywork in a safe and supportive setting—holotropic breathwork integrates the insights from modern consciousness research, depth psychology, transpersonal psychology, anthropology, Eastern spiritual practices, and mystical traditions. The Grofs' work with holotropic states of consciousness has introduced revolutionary changes to psychiatry, psychology, and psychotherapy. Written in a clear, easily understandable style, this indispensable book summarizes their remarkable insights. The second edition includes an expanded section on the history of holotropic breathwork, as well as information on Grof® Legacy Training.
Author:
Publisher:
ISBN:
Category : Encyclopedias and dictionaries
Languages : en
Pages : 468
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Book Description
Author: Carlos Algora
Publisher: John Wiley & Sons
ISBN: 1118472969
Category : Technology & Engineering
Languages : en
Pages : 806
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Book Description
Concentrator Photovoltaics (CPV) is one of the most promising technologies to produce solar electricity at competitive prices. High performing CPV systems with efficiencies well over 30% and multi-megawatt CPV plants are now a reality. As a result of these achievements, the global CPV market is expected to grow dramatically over the next few years reaching cumulative installed capacity of 12.5 GW by 2020. In this context, both new and consolidated players are moving fast to gain a strategic advantage in this emerging market. Written with clear, brief and self-contained technical explanations, Handbook of Concentrator Photovoltaic Technology provides a complete overview of CPV covering: the fundamentals of solar radiation, solar cells, concentrator optics, modules and trackers; all aspects of characterization and reliability; case studies based on the description of actual systems and plants in the field; environmental impact, market potential and cost analysis. CPV technology is at a key point of expansion. This timely handbook aims to provide a comprehensive assessment of all CPV scientific, technological and engineering background with a view to equipping engineers and industry professionals with all of the vital information they need to help them sustain the impetus of this encouraging technology. Key features: Uniquely combines an explanation of the fundamentals of CPV systems and components with an overview of the market place and their real-life applications. Each chapter is written by well-known industry specialists with extensive expertise in each particular field of CPV technology. Reviews the basic concepts of multi-junction solar cells and new concepts for CPV cells, highlighting the key differences between them. Demonstrates the state of the art of several CPV centres and companies. Facilitates future cost calculation models for CPV. Features extensive case studies in each chapter, including coverage of CPV modules and systems.
