Treks Into Intuitive Geometry

Author : J. Akiyama
Publisher : Springer Nature
Page : 642 pages
File Size : 49,9 Mb
Release : 2024
Category : Geometry
ISBN : 9789819986088

Get Book

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 : Jin Akiyama,Kiyoko Matsunaga
Publisher : Unknown
Page : 128 pages
File Size : 43,8 Mb
Release : 2015
Category : Electronic
ISBN : 443155842X

Get Book

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 : Imre Bárány,K. Böröczky
Publisher : Unknown
Page : 456 pages
File Size : 41,6 Mb
Release : 1997
Category : Geometry
ISBN : UOM:39015050320566

Get Book

Intuitive Geometry by Imre Bárány,K. Böröczky Pdf

Author : K. Böröczky,G. Fejes Tóth
Publisher : Unknown
Page : 708 pages
File Size : 40,9 Mb
Release : 1987
Category : Electronic
ISBN : OCLC:256113099

Get Book

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

Author : Jost-Hinrich Eschenburg
Publisher : Springer Nature
Page : 168 pages
File Size : 54,7 Mb
Release : 2022-10-31
Category : Mathematics
ISBN : 9783658386405

Get Book

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 : Hallard T. Croft,Kenneth Falconer,Richard K. Guy
Publisher : Springer Science & Business Media
Page : 213 pages
File Size : 49,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461209638

Get Book

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 : Jin Akiyama,Hiro Ito,Toshinori Sakai,Yushi Uno
Publisher : Springer
Page : 306 pages
File Size : 44,7 Mb
Release : 2016-11-24
Category : Computers
ISBN : 9783319485324

Get Book

Discrete and Computational Geometry and Graphs by Jin Akiyama,Hiro Ito,Toshinori Sakai,Yushi Uno Pdf

This book constitutes the thoroughly refereed post-conference proceedings of the 18th Japanese Conference on Discrete and Computational Geometry and Graphs, JDCDGG 2015, held in Kyoto, Japan, in September 2015. The total of 25 papers included in this volume was carefully reviewed and selected from 64 submissions. The papers feature advances made in the field of computational geometry and focus on emerging technologies, new methodology and applications, graph theory and dynamics. This proceedings are dedicated to Naoki Katoh on the occasion of his retirement from Kyoto University.

Author : Viktor Vasilʹevich Prasolov
Publisher : American Mathematical Soc.
Page : 106 pages
File Size : 51,8 Mb
Release : 1995
Category : Mathematics
ISBN : 9780821803561

Get Book

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 : School Mathematics Study Group,Richard D. Anderson
Publisher : Unknown
Page : 227 pages
File Size : 52,8 Mb
Release : 1961
Category : Geometry
ISBN : OCLC:165935

Get Book

Intuitive Geometry by School Mathematics Study Group,Richard D. Anderson Pdf

Author : Nathalie Strassburg
Publisher : Nathalie Strassburg
Page : 156 pages
File Size : 46,5 Mb
Release : 2024-06-26
Category : Art
ISBN : 9781928538998

Get Book

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 : Strassburg
Publisher : Unknown
Page : 118 pages
File Size : 45,7 Mb
Release : 2021-12-17
Category : Electronic
ISBN : 1928538983

Get Book

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 : Nam-Hoon Lee
Publisher : Springer Nature
Page : 264 pages
File Size : 46,9 Mb
Release : 2020-04-28
Category : Mathematics
ISBN : 9783030421014

Get Book

Geometry: from Isometries to Special Relativity by Nam-Hoon Lee Pdf

This textbook offers a geometric perspective on special relativity, bridging Euclidean space, hyperbolic space, and Einstein’s spacetime in one accessible, self-contained volume. Using tools tailored to undergraduates, the author explores Euclidean and non-Euclidean geometries, gradually building from intuitive to abstract spaces. By the end, readers will have encountered a range of topics, from isometries to the Lorentz–Minkowski plane, building an understanding of how geometry can be used to model special relativity. Beginning with intuitive spaces, such as the Euclidean plane and the sphere, a structure theorem for isometries is introduced that serves as a foundation for increasingly sophisticated topics, such as the hyperbolic plane and the Lorentz–Minkowski plane. By gradually introducing tools throughout, the author offers readers an accessible pathway to visualizing increasingly abstract geometric concepts. Numerous exercises are also included with selected solutions provided. Geometry: from Isometries to Special Relativity offers a unique approach to non-Euclidean geometries, culminating in a mathematical model for special relativity. The focus on isometries offers undergraduates an accessible progression from the intuitive to abstract; instructors will appreciate the complete instructor solutions manual available online. A background in elementary calculus is assumed.

Author : David Gay
Publisher : Wiley
Page : 0 pages
File Size : 49,6 Mb
Release : 1997-09-17
Category : Mathematics
ISBN : 0471041777

Get Book

Geometry by Discovery by David Gay Pdf

Designed for use within a junior/senior level geometry course, the topics covered in this text will enable the student to enhance their geometric skills, solve problems with a variety of old and new techniques (constructing models, conjectures, guessing, drawing pictures, etc.) and see how mathematical ideas are connected (similar solutions to solve different problems). Each chapter provides exercises, notes and a list of references for further reading.

Author : Margaret Wiscamb Hutchinson
Publisher : Merrill Publishing Company
Page : 324 pages
File Size : 50,7 Mb
Release : 1972-01-01
Category : Geometry
ISBN : 0675094275

Get Book

Geometry: an Intuitive Approach by Margaret Wiscamb Hutchinson Pdf

Author : Nathalie Strassburg
Publisher : Unknown
Page : 118 pages
File Size : 54,8 Mb
Release : 2021-01-27
Category : Electronic
ISBN : 1928538975

Get Book

Intuitive Geometry 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 book includes the method with step by step instructions, step by step examples and artwork to showcase the method.