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This book is written in a style that uncovers the mathematical theories buried in our everyday lives such as examples from patterns that appear in nature, art, and traditional crafts, and in mathematical mechanisms in techniques used by architects. The authors believe that through dialogues between students and mathematicians, readers may discover the processes by which the founders of the theories came to their various conclusions―their trials, errors, tribulations, and triumphs. The goal is for readers to refine their mathematical sense of how to find good questions and how to grapple with these problems. Another aim is to provide enjoyment in the process of applying mathematical rules to beautiful art and design by examples that highlight the wonders and mysteries from our daily lives. To fulfill these aims, this book deals with the latest unique and beautiful results in polygons and polyhedra and the dynamism of geometrical research history that can be found around us. The term "intuitive geometry" was coined by Lászlo Fejes Tóth to refer to the kind of geometry which, in Hilbert's words, can be explained to and appeal to the "man on the street." This book allows people to enjoy intuitive geometry informally and instinctively. It does not require more than a high school level of knowledge but calls for a sense of wonder, intuition, and mathematical maturity.
Book Synopsis Treks into Intuitive Geometry by : Jin Akiyama
Download or read book Treks into Intuitive Geometry written by Jin Akiyama and published by Springer. This book was released on 2015-12-04 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is written in a style that uncovers the mathematical theories buried in our everyday lives such as examples from patterns that appear in nature, art, and traditional crafts, and in mathematical mechanisms in techniques used by architects. The authors believe that through dialogues between students and mathematicians, readers may discover the processes by which the founders of the theories came to their various conclusions―their trials, errors, tribulations, and triumphs. The goal is for readers to refine their mathematical sense of how to find good questions and how to grapple with these problems. Another aim is to provide enjoyment in the process of applying mathematical rules to beautiful art and design by examples that highlight the wonders and mysteries from our daily lives. To fulfill these aims, this book deals with the latest unique and beautiful results in polygons and polyhedra and the dynamism of geometrical research history that can be found around us. The term "intuitive geometry" was coined by Lászlo Fejes Tóth to refer to the kind of geometry which, in Hilbert's words, can be explained to and appeal to the "man on the street." This book allows people to enjoy intuitive geometry informally and instinctively. It does not require more than a high school level of knowledge but calls for a sense of wonder, intuition, and mathematical maturity.
The Intuitive Geometry method is a basic set of principles for using overlapping circles to create and design anything. The method includes the circle, square, triangle, hexagon, pentagon, spirals, waves, and scaling. The book includes the method with step by step instructions, step by step examples and artwork to showcase the method.
Book Synopsis Intuitive Geometry by : Strassburg
Download or read book Intuitive Geometry written by Strassburg and published by . This book was released on 2021-12-17 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Intuitive Geometry method is a basic set of principles for using overlapping circles to create and design anything. The method includes the circle, square, triangle, hexagon, pentagon, spirals, waves, and scaling. The book includes the method with step by step instructions, step by step examples and artwork to showcase the method.
Mathematicians and non-mathematicians alike have long been fascinated by geometrical problems, particularly those that are intuitive in the sense of being easy to state, perhaps with the aid of a simple diagram. Each section in the book describes a problem or a group of related problems. Usually the problems are capable of generalization of variation in many directions. The book can be appreciated at many levels and is intended for everyone from amateurs to research mathematicians.
Book Synopsis Unsolved Problems in Geometry by : Hallard T. Croft
Download or read book Unsolved Problems in Geometry written by Hallard T. Croft and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematicians and non-mathematicians alike have long been fascinated by geometrical problems, particularly those that are intuitive in the sense of being easy to state, perhaps with the aid of a simple diagram. Each section in the book describes a problem or a group of related problems. Usually the problems are capable of generalization of variation in many directions. The book can be appreciated at many levels and is intended for everyone from amateurs to research mathematicians.
This volume contains 17 surveys that cover many recent developments in Discrete Geometry and related fields. Besides presenting the state-of-the-art of classical research subjects like packing and covering, it also offers an introduction to new topological, algebraic and computational methods in this very active research field. The readers will find a variety of modern topics and many fascinating open problems that may serve as starting points for research.
Book Synopsis New Trends in Intuitive Geometry by : Gergely Ambrus
Download or read book New Trends in Intuitive Geometry written by Gergely Ambrus and published by Springer. This book was released on 2018-11-03 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains 17 surveys that cover many recent developments in Discrete Geometry and related fields. Besides presenting the state-of-the-art of classical research subjects like packing and covering, it also offers an introduction to new topological, algebraic and computational methods in this very active research field. The readers will find a variety of modern topics and many fascinating open problems that may serve as starting points for research.
This book is written in a style that uncovers the mathematical theories hidden in our daily lives, using examples of patterns that appear in nature, arts, traditional crafts, as well as mathematical mechanics in architectural techniques. The authors believe that through conversations between students and mathematicians, readers may learn about the methods used by the originators of these theoriestheir trials, errors, and triumphsin reaching their various conclusions. The goal is to help readers refine their mathematical sense in terms of formulating valuable questions and pursuing them. In addition, the book aims to provide enjoyment in the application of mathematical principles to beautiful art and design by using examples that highlight the wonders and mysteries of these works found in our daily lives. To achieve these goals, the book tackles the latest exquisite results on polygons and polyhedra and the dynamic history of geometric research found around us. The term "intuitive geometry" was coined by Lszlo Fejes Tth and refers to the kind of geometry which, in Hilbert's words, can be explained to and appeal to the "man on the street." This book enables readers to enjoy intuitive geometry informally and instinctively. It does not require more than a high school level of knowledge but calls for a sense of wonder, intuition, and mathematical maturity. In this second edition, many new results, and elegant proofs on a variety of topics have been added, enhancing the books rich content even further.
Book Synopsis Treks Into Intuitive Geometry by : J. Akiyama
Download or read book Treks Into Intuitive Geometry written by J. Akiyama and published by Springer Nature. This book was released on 2024 with total page 642 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is written in a style that uncovers the mathematical theories hidden in our daily lives, using examples of patterns that appear in nature, arts, traditional crafts, as well as mathematical mechanics in architectural techniques. The authors believe that through conversations between students and mathematicians, readers may learn about the methods used by the originators of these theoriestheir trials, errors, and triumphsin reaching their various conclusions. The goal is to help readers refine their mathematical sense in terms of formulating valuable questions and pursuing them. In addition, the book aims to provide enjoyment in the application of mathematical principles to beautiful art and design by using examples that highlight the wonders and mysteries of these works found in our daily lives. To achieve these goals, the book tackles the latest exquisite results on polygons and polyhedra and the dynamic history of geometric research found around us. The term "intuitive geometry" was coined by Lszlo Fejes Tth and refers to the kind of geometry which, in Hilbert's words, can be explained to and appeal to the "man on the street." This book enables readers to enjoy intuitive geometry informally and instinctively. It does not require more than a high school level of knowledge but calls for a sense of wonder, intuition, and mathematical maturity. In this second edition, many new results, and elegant proofs on a variety of topics have been added, enhancing the books rich content even further.
This remarkable book has endured as a true masterpiece of mathematical exposition. There are few mathematics books that are still so widely read and continue to have so much to offer—even after more than half a century has passed! The book is overflowing with mathematical ideas, which are always explained clearly and elegantly, and above all, with penetrating insight. It is a joy to read, both for beginners and experienced mathematicians. “Hilbert and Cohn-Vossen” is full of interesting facts, many of which you wish you had known before. It's also likely that you have heard those facts before, but surely wondered where they could be found. The book begins with examples of the simplest curves and surfaces, including thread constructions of certain quadrics and other surfaces. The chapter on regular systems of points leads to the crystallographic groups and the regular polyhedra in R 3 R3. In this chapter, they also discuss plane lattices. By considering unit lattices, and throwing in a small amount of number theory when necessary, they effortlessly derive Leibniz's series: π/4=1−1/3+1/5−1/7+−… π/4=1−1/3+1/5−1/7+−…. In the section on lattices in three and more dimensions, the authors consider sphere-packing problems, including the famous Kepler problem. One of the most remarkable chapters is “Projective Configurations”. In a short introductory section, Hilbert and Cohn-Vossen give perhaps the most concise and lucid description of why a general geometer would care about projective geometry and why such an ostensibly plain setup is truly rich in structure and ideas. Here, we see regular polyhedra again, from a different perspective. One of the high points of the chapter is the discussion of Schlafli's Double-Six, which leads to the description of the 27 lines on the general smooth cubic surface. As is true throughout the book, the magnificent drawings in this chapter immeasurably help the reader. A particularly intriguing section in the chapter on differential geometry is Eleven Properties of the Sphere. Which eleven properties of such a ubiquitous mathematical object caught their discerning eye and why? Many mathematicians are familiar with the plaster models of surfaces found in many mathematics departments. The book includes pictures of some of the models that are found in the Göttingen collection. Furthermore, the mysterious lines that mark these surfaces are finally explained! The chapter on kinematics includes a nice discussion of linkages and the geometry of configurations of points and rods that are connected and, perhaps, constrained in some way. This topic in geometry has become increasingly important in recent times, especially in applications to robotics. This is another example of a simple situation that leads to a rich geometry. It would be hard to overestimate the continuing influence Hilbert-Cohn-Vossen's book has had on mathematicians of this century. It surely belongs in the “pantheon” of great mathematics books.
Book Synopsis Geometry and the Imagination by : D. Hilbert
Download or read book Geometry and the Imagination written by D. Hilbert and published by American Mathematical Soc.. This book was released on 2021-03-17 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: This remarkable book has endured as a true masterpiece of mathematical exposition. There are few mathematics books that are still so widely read and continue to have so much to offer—even after more than half a century has passed! The book is overflowing with mathematical ideas, which are always explained clearly and elegantly, and above all, with penetrating insight. It is a joy to read, both for beginners and experienced mathematicians. “Hilbert and Cohn-Vossen” is full of interesting facts, many of which you wish you had known before. It's also likely that you have heard those facts before, but surely wondered where they could be found. The book begins with examples of the simplest curves and surfaces, including thread constructions of certain quadrics and other surfaces. The chapter on regular systems of points leads to the crystallographic groups and the regular polyhedra in R 3 R3. In this chapter, they also discuss plane lattices. By considering unit lattices, and throwing in a small amount of number theory when necessary, they effortlessly derive Leibniz's series: π/4=1−1/3+1/5−1/7+−… π/4=1−1/3+1/5−1/7+−…. In the section on lattices in three and more dimensions, the authors consider sphere-packing problems, including the famous Kepler problem. One of the most remarkable chapters is “Projective Configurations”. In a short introductory section, Hilbert and Cohn-Vossen give perhaps the most concise and lucid description of why a general geometer would care about projective geometry and why such an ostensibly plain setup is truly rich in structure and ideas. Here, we see regular polyhedra again, from a different perspective. One of the high points of the chapter is the discussion of Schlafli's Double-Six, which leads to the description of the 27 lines on the general smooth cubic surface. As is true throughout the book, the magnificent drawings in this chapter immeasurably help the reader. A particularly intriguing section in the chapter on differential geometry is Eleven Properties of the Sphere. Which eleven properties of such a ubiquitous mathematical object caught their discerning eye and why? Many mathematicians are familiar with the plaster models of surfaces found in many mathematics departments. The book includes pictures of some of the models that are found in the Göttingen collection. Furthermore, the mysterious lines that mark these surfaces are finally explained! The chapter on kinematics includes a nice discussion of linkages and the geometry of configurations of points and rods that are connected and, perhaps, constrained in some way. This topic in geometry has become increasingly important in recent times, especially in applications to robotics. This is another example of a simple situation that leads to a rich geometry. It would be hard to overestimate the continuing influence Hilbert-Cohn-Vossen's book has had on mathematicians of this century. It surely belongs in the “pantheon” of great mathematics books.
Download or read book Basic Mathematics written by Serge Lang and published by . This book was released on 1988-01 with total page 475 pages. Available in PDF, EPUB and Kindle. Book excerpt:
For mathematicians or others who wish to keep up to date with the state of the art of geometrical problems, this collection of problems that are easy to state and understand but are as yet unsolved covers a wide variety of topics including convex sets, polyhedra, packing and covering, tiling, and combinatorial problems. Annotation copyrighted by Book News, Inc., Portland, OR.
Book Synopsis Unsolved Problems in Geometry by : Hallard T. Croft
Download or read book Unsolved Problems in Geometry written by Hallard T. Croft and published by New York : Springer-Verlag. This book was released on 1991 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: For mathematicians or others who wish to keep up to date with the state of the art of geometrical problems, this collection of problems that are easy to state and understand but are as yet unsolved covers a wide variety of topics including convex sets, polyhedra, packing and covering, tiling, and combinatorial problems. Annotation copyrighted by Book News, Inc., Portland, OR.
This book deals with the geometry of visual space in all its aspects. As in any branch of mathematics, the aim is to trace the hidden to the obvious; the peculiarity of geometry is that the obvious is sometimes literally before one's eyes.Starting from intuition, spatial concepts are embedded in the pre-existing mathematical framework of linear algebra and calculus. The path from visualization to mathematically exact language is itself the learning content of this book. This is intended to close an often lamented gap in understanding between descriptive preschool and school geometry and the abstract concepts of linear algebra and calculus. At the same time, descriptive geometric modes of argumentation are justified because their embedding in the strict mathematical language has been clarified. The concepts of geometry are of a very different nature; they denote, so to speak, different layers of geometric thinking: some arguments use only concepts such as point, straight line, and incidence, others require angles and distances, still others symmetry considerations. Each of these conceptual fields determines a separate subfield of geometry and a separate chapter of this book, with the exception of the last-mentioned conceptual field "symmetry", which runs through all the others: - Incidence: Projective geometry - Parallelism: Affine geometry - Angle: Conformal Geometry - Distance: Metric Geometry - Curvature: Differential Geometry - Angle as distance measure: Spherical and Hyperbolic Geometry - Symmetry: Mapping Geometry. The mathematical experience acquired in the visual space can be easily transferred to much more abstract situations with the help of the vector space notion. The generalizations beyond the visual dimension point in two directions: Extension of the number concept and transcending the three illustrative dimensions. This book is a translation of the original German 1st edition Geometrie – Anschauung und Begriffe by Jost-Hinrich Eschenburg, published by Springer Fachmedien Wiesbaden GmbH, part of Springer Nature in 2020. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation. Springer Nature works continuously to further the development of tools for the production of books and on the related technologies to support the authors.
Book Synopsis Geometry - Intuition and Concepts by : Jost-Hinrich Eschenburg
Download or read book Geometry - Intuition and Concepts written by Jost-Hinrich Eschenburg and published by Springer Nature. This book was released on 2022-10-31 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the geometry of visual space in all its aspects. As in any branch of mathematics, the aim is to trace the hidden to the obvious; the peculiarity of geometry is that the obvious is sometimes literally before one's eyes.Starting from intuition, spatial concepts are embedded in the pre-existing mathematical framework of linear algebra and calculus. The path from visualization to mathematically exact language is itself the learning content of this book. This is intended to close an often lamented gap in understanding between descriptive preschool and school geometry and the abstract concepts of linear algebra and calculus. At the same time, descriptive geometric modes of argumentation are justified because their embedding in the strict mathematical language has been clarified. The concepts of geometry are of a very different nature; they denote, so to speak, different layers of geometric thinking: some arguments use only concepts such as point, straight line, and incidence, others require angles and distances, still others symmetry considerations. Each of these conceptual fields determines a separate subfield of geometry and a separate chapter of this book, with the exception of the last-mentioned conceptual field "symmetry", which runs through all the others: - Incidence: Projective geometry - Parallelism: Affine geometry - Angle: Conformal Geometry - Distance: Metric Geometry - Curvature: Differential Geometry - Angle as distance measure: Spherical and Hyperbolic Geometry - Symmetry: Mapping Geometry. The mathematical experience acquired in the visual space can be easily transferred to much more abstract situations with the help of the vector space notion. The generalizations beyond the visual dimension point in two directions: Extension of the number concept and transcending the three illustrative dimensions. This book is a translation of the original German 1st edition Geometrie – Anschauung und Begriffe by Jost-Hinrich Eschenburg, published by Springer Fachmedien Wiesbaden GmbH, part of Springer Nature in 2020. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation. Springer Nature works continuously to further the development of tools for the production of books and on the related technologies to support the authors.
The present volume is a collection of a dozen survey articles, dedicated to the memory of the famous Hungarian geometer, László Fejes Tóth, on the 99th anniversary of his birth. Each article reviews recent progress in an important field in intuitive, discrete, and convex geometry. The mathematical work and perspectives of all editors and most contributors of this volume were deeply influenced by László Fejes Tóth.
Book Synopsis Geometry - Intuitive, Discrete, and Convex by : Imre Bárány
Download or read book Geometry - Intuitive, Discrete, and Convex written by Imre Bárány and published by Springer. This book was released on 2015-04-09 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume is a collection of a dozen survey articles, dedicated to the memory of the famous Hungarian geometer, László Fejes Tóth, on the 99th anniversary of his birth. Each article reviews recent progress in an important field in intuitive, discrete, and convex geometry. The mathematical work and perspectives of all editors and most contributors of this volume were deeply influenced by László Fejes Tóth.