Intuitive Geometries

Author : Jin Akiyama,Kiyoko Matsunaga
Publisher : Springer
Page : 425 pages
File Size : 41,7 Mb
Release : 2015-12-04
Category : Mathematics
ISBN : 9784431558439

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Treks into Intuitive Geometry by Jin Akiyama,Kiyoko Matsunaga Pdf

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.

Author : Strassburg
Publisher : Unknown
Page : 118 pages
File Size : 52,7 Mb
Release : 2021-12-17
Category : Electronic
ISBN : 1928538983

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Intuitive Geometry by Strassburg Pdf

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.

Author : J. Akiyama
Publisher : Springer Nature
Page : 642 pages
File Size : 46,8 Mb
Release : 2024
Category : Geometry
ISBN : 9789819986088

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Treks Into Intuitive Geometry by J. Akiyama Pdf

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.

Author : Gergely Ambrus,Imre Bárány,Károly J. Böröczky,Gábor Fejes Tóth,János Pach
Publisher : Springer
Page : 458 pages
File Size : 45,9 Mb
Release : 2018-11-03
Category : Mathematics
ISBN : 9783662574133

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New Trends in Intuitive Geometry by Gergely Ambrus,Imre Bárány,Károly J. Böröczky,Gábor Fejes Tóth,János Pach Pdf

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.

Author : Nathalie Strassburg
Publisher : Nathalie Strassburg
Page : 156 pages
File Size : 53,8 Mb
Release : 2024-07-02
Category : Art
ISBN : 9781928538998

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Intuitive Geometry: Drawing with overlapping circles - 2nd Edition by Nathalie Strassburg Pdf

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 2nd Edition of the book includes more detailed step by step instructions for the Intuitive Geometry method, ten examples of applying the method with detailed step by step instructions, and forty artworks to showcase the Intuitive Geometry method. The ten examples are: Bees, Butterflies, Flowers (3 fold), Flowers (4 fold), Flowers (5 fold), Human Body, Human Eye, Human Face, Snowflakes, and Spiders. For more information visit www.nathaliestrassburg.com.

Author : Imre Bárány,Károly Jr. Böröczky,Gábor Fejes Tóth,Janos Pach
Publisher : Springer
Page : 384 pages
File Size : 46,9 Mb
Release : 2015-04-09
Category : Mathematics
ISBN : 9783642414985

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Geometry - Intuitive, Discrete, and Convex by Imre Bárány,Károly Jr. Böröczky,Gábor Fejes Tóth,Janos Pach Pdf

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.

Author : Imre Bárány,K. Böröczky
Publisher : Unknown
Page : 456 pages
File Size : 45,9 Mb
Release : 1997
Category : Geometry
ISBN : UOM:39015050320566

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Intuitive Geometry by Imre Bárány,K. Böröczky Pdf

Author : Jost-Hinrich Eschenburg
Publisher : Springer Nature
Page : 168 pages
File Size : 48,8 Mb
Release : 2022-10-31
Category : Mathematics
ISBN : 9783658386405

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Geometry - Intuition and Concepts by Jost-Hinrich Eschenburg Pdf

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.

Author : Emily Carson,Renate Huber
Publisher : Springer Science & Business Media
Page : 328 pages
File Size : 48,8 Mb
Release : 2006-07-02
Category : Philosophy
ISBN : 9781402040405

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Intuition and the Axiomatic Method by Emily Carson,Renate Huber Pdf

Following developments in modern geometry, logic and physics, many scientists and philosophers in the modern era considered Kant’s theory of intuition to be obsolete. But this only represents one side of the story concerning Kant, intuition and twentieth century science. Several prominent mathematicians and physicists were convinced that the formal tools of modern logic, set theory and the axiomatic method are not sufficient for providing mathematics and physics with satisfactory foundations. All of Hilbert, Gödel, Poincaré, Weyl and Bohr thought that intuition was an indispensable element in describing the foundations of science. They had very different reasons for thinking this, and they had very different accounts of what they called intuition. But they had in common that their views of mathematics and physics were significantly influenced by their readings of Kant. In the present volume, various views of intuition and the axiomatic method are explored, beginning with Kant’s own approach. By way of these investigations, we hope to understand better the rationale behind Kant’s theory of intuition, as well as to grasp many facets of the relations between theories of intuition and the axiomatic method, dealing with both their strengths and limitations; in short, the volume covers logical and non-logical, historical and systematic issues in both mathematics and physics.

Author : A. W. Carus,Michael Friedman,Wolfgang Kienzler,Sven Schlotter,Alan Richardson
Publisher : Oxford University Press, USA
Page : 516 pages
File Size : 55,6 Mb
Release : 2019-04-10
Category : Philosophy
ISBN : 9780198748403

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Rudolf Carnap, Early Writings by A. W. Carus,Michael Friedman,Wolfgang Kienzler,Sven Schlotter,Alan Richardson Pdf

This is the first volume of the Complete Writings of Rudolf Carnap, which brings together the works of a great twentieth-century philosopher whose work has enjoyed renewed interest and increasing influence since the 1990s. Carnap's early writings are translated into English for the first time, supplied here with an introduction and extensive notes which place the text in the relevant scientific and historical contexts. Edited by an international team ofscholars who specialize in different aspects of Carnap's thought, the availability of these texts in English will completely revise the general understanding of this important philosopher and his ideas.

Author : K. Böröczky,G. Fejes Tóth
Publisher : Unknown
Page : 708 pages
File Size : 54,8 Mb
Release : 1987
Category : Electronic
ISBN : OCLC:256113099

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Intuitive Geometry by K. Böröczky,G. Fejes Tóth Pdf

Author : Hallard T. Croft,Kenneth Falconer,Richard K. Guy
Publisher : Springer Science & Business Media
Page : 213 pages
File Size : 47,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461209638

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Unsolved Problems in Geometry by Hallard T. Croft,Kenneth Falconer,Richard K. Guy Pdf

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.

Author : Efraim Fischbein
Publisher : Springer Science & Business Media
Page : 234 pages
File Size : 46,9 Mb
Release : 2005-12-19
Category : Education
ISBN : 9780306472374

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Intuition in Science and Mathematics by Efraim Fischbein Pdf

In writing the present book I have had in mind the following objectives: - To propose a theoretical, comprehensive view of the domain of intuition. - To identify and organize the experimental findings related to intuition scattered in a wide variety of research contexts. - To reveal the educational implications of the idea, developed for science and mathematics education. Most of the existing monographs in the field of intuition are mainly concerned with theoretical debates - definitions, philosophical attitudes, historical considerations. (See, especially the works of Wild (1938), of Bunge (1 962) and of Noddings and Shore (1 984).) A notable exception is the book by Westcott (1968), which combines theoretical analyses with the author’s own experimental studies. But, so far, no attempt has been made to identify systematically those findings, spread throughout the research literature, which could contribute to the deciphering of the mechanisms of intuition. Very often the relevant studies do not refer explicitly to intuition. Even when this term is used it occurs, usually, as a self-evident, common sense term.

Author : Viktor Vasilʹevich Prasolov
Publisher : American Mathematical Soc.
Page : 106 pages
File Size : 41,5 Mb
Release : 1995
Category : Mathematics
ISBN : 9780821803561

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Intuitive Topology by Viktor Vasilʹevich Prasolov Pdf

This book is an introduction to elementary topology presented in an intuitive way, emphasizing the visual aspect. Examples of nontrivial and often unexpected topological phenomena acquaint the reader with the picturesque world of knots, links, vector fields, and two-dimensional surfaces. The book begins with definitions presented in a tangible and perceptible way, on an everyday level, and progressively makes them more precise and rigorous, eventually reaching the level of fairly sophisticated proofs. This allows meaningful problems to be tackled from the outset. Another unusual trait of this book is that it deals mainly with constructions and maps, rather than with proofs that certain maps and constructions do or do not exist. The numerous illustrations are an essential feature. The book is accessible not only to undergraduates but also to high school students and will interest any reader who has some feeling for the visual elegance of geometry and topology.

Author : Ivor Grattan-Guinness
Publisher : Elsevier
Page : 1040 pages
File Size : 52,5 Mb
Release : 2005-02-11
Category : Mathematics
ISBN : 0080457444

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Landmark Writings in Western Mathematics 1640-1940 by Ivor Grattan-Guinness Pdf

This book contains around 80 articles on major writings in mathematics published between 1640 and 1940. All aspects of mathematics are covered: pure and applied, probability and statistics, foundations and philosophy. Sometimes two writings from the same period and the same subject are taken together. The biography of the author(s) is recorded, and the circumstances of the preparation of the writing are given. When the writing is of some lengths an analytical table of its contents is supplied. The contents of the writing is reviewed, and its impact described, at least for the immediate decades. Each article ends with a bibliography of primary and secondary items. First book of its kind Covers the period 1640-1940 of massive development in mathematics Describes many of the main writings of mathematics Articles written by specialists in their field