Two Dimensional Spaces

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Topology as Fluid Geometry

Author : James W. Cannon
Publisher : American Mathematical Soc.
ISBN 13 : 1470437155
Total Pages : 181 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Topology as Fluid Geometry by : James W. Cannon

Download or read book Topology as Fluid Geometry written by James W. Cannon and published by American Mathematical Soc.. This book was released on 2017 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second of a three volume collection devoted to the geometry, topology, and curvature of 2-dimensional spaces. The collection provides a guided tour through a wide range of topics by one of the twentieth century's masters of geometric topology. The books are accessible to college and graduate students and provide perspective and insight to mathematicians at all levels who are interested in geometry and topology. The second volume deals with the topology of 2-dimensional spaces. The attempts encountered in Volume 1 to understand length and area in the plane lead to examples most easily described by the methods of topology (fluid geometry): finite curves of infinite length, 1-dimensional curves of positive area, space-filling curves (Peano curves), 0-dimensional subsets of the plane through which no straight path can pass (Cantor sets), etc. Volume 2 describes such sets. All of the standard topological results about 2-dimensional spaces are then proved, such as the Fundamental Theorem of Algebra (two proofs), the No Retraction Theorem, the Brouwer Fixed Point Theorem, the Jordan Curve Theorem, the Open Mapping Theorem, the Riemann-Hurwitz Theorem, and the Classification Theorem for Compact 2-manifolds. Volume 2 also includes a number of theorems usually assumed without proof since their proofs are not readily available, for example, the Zippin Characterization Theorem for 2-dimensional spaces that are locally Euclidean, the Schoenflies Theorem characterizing the disk, the Triangulation Theorem for 2-manifolds, and the R. L. Moore's Decomposition Theorem so useful in understanding fractal sets.

Two-Dimensional Spaces, Volumes 1, 2, And 3

Author : JAMES W. CANNON
Publisher :
ISBN 13 : 9781470443238
Total Pages : 389 pages
Book Rating : 4.4/5 (432 download)

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Book Synopsis Two-Dimensional Spaces, Volumes 1, 2, And 3 by : JAMES W. CANNON

Download or read book Two-Dimensional Spaces, Volumes 1, 2, And 3 written by JAMES W. CANNON and published by . This book was released on 2018-02-28 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: This three-volume collection is devoted to the geometry, topology, and curvature of 2-dimensional spaces. The collection provides a guided tour through a wide range of topics by one of the twentieth century's masters of geometric topology. The books are accessible to college and graduate students and provide perspective and insight to mathematicians at all levels who are interested in geometry and topology.

The Planiverse

Author : A.K. Dewdney
Publisher : Springer Science & Business Media
ISBN 13 : 1461301998
Total Pages : 273 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis The Planiverse by : A.K. Dewdney

Download or read book The Planiverse written by A.K. Dewdney and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: A classic book about life in a two-dimensional universe, written by a well-known author. Now brought back into print in this revised and updated edition, the book is written within the great tradition of Abbott's Flatland, and Hinton's famous Sphereland. Accessible, imaginative, and clever, it will appeal to a wide array of readers, from serious mathematicians and computer scientists, to science fiction fans.

Geometry of Lengths, Areas, and Volumes

Author : James W. Cannon
Publisher : American Mathematical Soc.
ISBN 13 : 1470437147
Total Pages : 133 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Geometry of Lengths, Areas, and Volumes by : James W. Cannon

Download or read book Geometry of Lengths, Areas, and Volumes written by James W. Cannon and published by American Mathematical Soc.. This book was released on 2017-11-16 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first of a three volume collection devoted to the geometry, topology, and curvature of 2-dimensional spaces. The collection provides a guided tour through a wide range of topics by one of the twentieth century's masters of geometric topology. The books are accessible to college and graduate students and provide perspective and insight to mathematicians at all levels who are interested in geometry and topology. The first volume begins with length measurement as dominated by the Pythagorean Theorem (three proofs) with application to number theory; areas measured by slicing and scaling, where Archimedes uses the physical weights and balances to calculate spherical volume and is led to the invention of calculus; areas by cut and paste, leading to the Bolyai-Gerwien theorem on squaring polygons; areas by counting, leading to the theory of continued fractions, the efficient rational approximation of real numbers, and Minkowski's theorem on convex bodies; straight-edge and compass constructions, giving complete proofs, including the transcendence of and , of the impossibility of squaring the circle, duplicating the cube, and trisecting the angle; and finally to a construction of the Hausdorff-Banach-Tarski paradox that shows some spherical sets are too complicated and cloudy to admit a well-defined notion of area.

Understanding High-Dimensional Spaces

Author : David B. Skillicorn
Publisher : Springer Science & Business Media
ISBN 13 : 3642333982
Total Pages : 109 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Understanding High-Dimensional Spaces by : David B. Skillicorn

Download or read book Understanding High-Dimensional Spaces written by David B. Skillicorn and published by Springer Science & Business Media. This book was released on 2012-09-24 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: High-dimensional spaces arise as a way of modelling datasets with many attributes. Such a dataset can be directly represented in a space spanned by its attributes, with each record represented as a point in the space with its position depending on its attribute values. Such spaces are not easy to work with because of their high dimensionality: our intuition about space is not reliable, and measures such as distance do not provide as clear information as we might expect. There are three main areas where complex high dimensionality and large datasets arise naturally: data collected by online retailers, preference sites, and social media sites, and customer relationship databases, where there are large but sparse records available for each individual; data derived from text and speech, where the attributes are words and so the corresponding datasets are wide, and sparse; and data collected for security, defense, law enforcement, and intelligence purposes, where the datasets are large and wide. Such datasets are usually understood either by finding the set of clusters they contain or by looking for the outliers, but these strategies conceal subtleties that are often ignored. In this book the author suggests new ways of thinking about high-dimensional spaces using two models: a skeleton that relates the clusters to one another; and boundaries in the empty space between clusters that provide new perspectives on outliers and on outlying regions. The book will be of value to practitioners, graduate students and researchers.

A Two Dimensional Page Becomes Three Dimensional Space

Author : Eric T. Sims
Publisher :
ISBN 13 :
Total Pages : 60 pages
Book Rating : 4.:/5 (348 download)

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Book Synopsis A Two Dimensional Page Becomes Three Dimensional Space by : Eric T. Sims

Download or read book A Two Dimensional Page Becomes Three Dimensional Space written by Eric T. Sims and published by . This book was released on 1995 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Introduction to Art: Design, Context, and Meaning

Author : Pamela Sachant
Publisher : Good Press
ISBN 13 :
Total Pages : 614 pages
Book Rating : 4.8/5 (596 download)

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Book Synopsis Introduction to Art: Design, Context, and Meaning by : Pamela Sachant

Download or read book Introduction to Art: Design, Context, and Meaning written by Pamela Sachant and published by Good Press. This book was released on 2023-11-27 with total page 614 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Art: Design, Context, and Meaning offers a deep insight and comprehension of the world of Art. Contents: What is Art? The Structure of Art Significance of Materials Used in Art Describing Art - Formal Analysis, Types, and Styles of Art Meaning in Art - Socio-Cultural Contexts, Symbolism, and Iconography Connecting Art to Our Lives Form in Architecture Art and Identity Art and Power Art and Ritual Life - Symbolism of Space and Ritual Objects, Mortality, and Immortality Art and Ethics

Human Dimension and Interior Space

Author : Julius Panero
Publisher : Watson-Guptill
ISBN 13 : 0770434606
Total Pages : 322 pages
Book Rating : 4.7/5 (74 download)

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Book Synopsis Human Dimension and Interior Space by : Julius Panero

Download or read book Human Dimension and Interior Space written by Julius Panero and published by Watson-Guptill. This book was released on 2014-01-21 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of human body measurements on a comparative basis is known as anthropometrics. Its applicability to the design process is seen in the physical fit, or interface, between the human body and the various components of interior space. Human Dimension and Interior Space is the first major anthropometrically based reference book of design standards for use by all those involved with the physical planning and detailing of interiors, including interior designers, architects, furniture designers, builders, industrial designers, and students of design. The use of anthropometric data, although no substitute for good design or sound professional judgment should be viewed as one of the many tools required in the design process. This comprehensive overview of anthropometrics consists of three parts. The first part deals with the theory and application of anthropometrics and includes a special section dealing with physically disabled and elderly people. It provides the designer with the fundamentals of anthropometrics and a basic understanding of how interior design standards are established. The second part contains easy-to-read, illustrated anthropometric tables, which provide the most current data available on human body size, organized by age and percentile groupings. Also included is data relative to the range of joint motion and body sizes of children. The third part contains hundreds of dimensioned drawings, illustrating in plan and section the proper anthropometrically based relationship between user and space. The types of spaces range from residential and commercial to recreational and institutional, and all dimensions include metric conversions. In the Epilogue, the authors challenge the interior design profession, the building industry, and the furniture manufacturer to seriously explore the problem of adjustability in design. They expose the fallacy of designing to accommodate the so-called average man, who, in fact, does not exist. Using government data, including studies prepared by Dr. Howard Stoudt, Dr. Albert Damon, and Dr. Ross McFarland, formerly of the Harvard School of Public Health, and Jean Roberts of the U.S. Public Health Service, Panero and Zelnik have devised a system of interior design reference standards, easily understood through a series of charts and situation drawings. With Human Dimension and Interior Space, these standards are now accessible to all designers of interior environments.

Normal Two-dimensional Singularities

Author : Henry B. Laufer
Publisher : Princeton University Press
ISBN 13 : 9780691081007
Total Pages : 180 pages
Book Rating : 4.0/5 (81 download)

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Book Synopsis Normal Two-dimensional Singularities by : Henry B. Laufer

Download or read book Normal Two-dimensional Singularities written by Henry B. Laufer and published by Princeton University Press. This book was released on 1971-11-21 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: A survey, thorough and timely, of the singularities of two-dimensional normal complex analytic varieties, the volume summarizes the results obtained since Hirzebruch's thesis (1953) and presents new contributions. First, the singularity is resolved and shown to be classified by its resolution; then, resolutions are classed by the use of spaces with nilpotents; finally, the spaces with nilpotents are determined by means of the local ring structure of the singularity.

Sensor Technology: Concepts, Methodologies, Tools, and Applications

Author : Management Association, Information Resources
Publisher : IGI Global
ISBN 13 : 1799824551
Total Pages : 1618 pages
Book Rating : 4.7/5 (998 download)

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Book Synopsis Sensor Technology: Concepts, Methodologies, Tools, and Applications by : Management Association, Information Resources

Download or read book Sensor Technology: Concepts, Methodologies, Tools, and Applications written by Management Association, Information Resources and published by IGI Global. This book was released on 2020-02-07 with total page 1618 pages. Available in PDF, EPUB and Kindle. Book excerpt: Collecting and processing data is a necessary aspect of living in a technologically advanced society. Whether it’s monitoring events, controlling different variables, or using decision-making applications, it is important to have a system that is both inexpensive and capable of coping with high amounts of data. As the application of these networks becomes more common, it becomes imperative to evaluate their effectiveness as well as other opportunities for possible implementation in the future. Sensor Technology: Concepts, Methodologies, Tools, and Applications is a vital reference source that brings together new ways to process and monitor data and to put it to work in everything from intelligent transportation systems to healthcare to multimedia applications. It also provides inclusive coverage on the processing and applications of wireless communication, sensor networks, and mobile computing. Highlighting a range of topics such as internet of things, signal processing hardware, and wireless sensor technologies, this multi-volume book is ideally designed for research and development engineers, IT specialists, developers, graduate students, academics, and researchers.

Two-Dimensional Geometries: A Problem-Solving Approach

Author : C. Herbert Clemens
Publisher : American Mathematical Soc.
ISBN 13 : 1470447606
Total Pages : 142 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Two-Dimensional Geometries: A Problem-Solving Approach by : C. Herbert Clemens

Download or read book Two-Dimensional Geometries: A Problem-Solving Approach written by C. Herbert Clemens and published by American Mathematical Soc.. This book was released on 2019-03-20 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book on two-dimensional geometry uses a problem-solving approach to actively engage students in the learning process. The aim is to guide readers through the story of the subject, while giving them room to discover and partially construct the story themselves. The book bridges the study of plane geometry and the study of curves and surfaces of non-constant curvature in three-dimensional Euclidean space. One useful feature is that the book can be adapted to suit different audiences. The first half of the text covers plane geometry without and with Euclid's Fifth Postulate, followed by a brief synthetic treatment of spherical geometry through the excess angle formula. This part only requires a background in high school geometry and basic trigonometry and is suitable for a quarter course for future high school geometry teachers. A brief foray into the second half could complete a semester course. The second half of the text gives a uniform treatment of all the complete, simply connected, two-dimensional geometries of constant curvature, one geometry for each real number (its curvature), including their groups of isometries, geodesics, measures of lengths and areas, as well as formulas for areas of regions bounded by polygons in terms of the curvature of the geometry and the sum of the interior angles of the polygon. A basic knowledge of real linear algebra and calculus of several (real) variables is useful background for this portion of the text.

Two-dimensional Depiction of Space

Author : Garth Potts
Publisher :
ISBN 13 :
Total Pages : 26 pages
Book Rating : 4.:/5 (26 download)

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Book Synopsis Two-dimensional Depiction of Space by : Garth Potts

Download or read book Two-dimensional Depiction of Space written by Garth Potts and published by . This book was released on 1971 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Principles of Two-Dimensional Design

Author : Wucius Wong
Publisher : John Wiley & Sons
ISBN 13 : 9780471289609
Total Pages : 100 pages
Book Rating : 4.2/5 (896 download)

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Book Synopsis Principles of Two-Dimensional Design by : Wucius Wong

Download or read book Principles of Two-Dimensional Design written by Wucius Wong and published by John Wiley & Sons. This book was released on 1991-01-16 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understanding the elements of two-dimensional design and the infinite options available in organizing choices made are at the core of this book. Wong surveys all concepts of forms and structures, covering most situations in two-dimensional composition, formal or informal.

2-Dimensional Categories

Author : Niles Johnson
Publisher : Oxford University Press, USA
ISBN 13 : 0198871376
Total Pages : 636 pages
Book Rating : 4.1/5 (988 download)

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Book Synopsis 2-Dimensional Categories by : Niles Johnson

Download or read book 2-Dimensional Categories written by Niles Johnson and published by Oxford University Press, USA. This book was released on 2021-01-31 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt: 2-Dimensional Categories is an introduction to 2-categories and bicategories, assuming only the most elementary aspects of category theory.

A Basic Course in Algebraic Topology

Author : William S. Massey
Publisher : Springer
ISBN 13 : 1493990632
Total Pages : 448 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis A Basic Course in Algebraic Topology by : William S. Massey

Download or read book A Basic Course in Algebraic Topology written by William S. Massey and published by Springer. This book was released on 2019-06-28 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is intended for a course in algebraic topology at the beginning graduate level. The main topics covered are the classification of compact 2-manifolds, the fundamental group, covering spaces, singular homology theory, and singular cohomology theory. These topics are developed systematically, avoiding all unnecessary definitions, terminology, and technical machinery. The text consists of material from the first five chapters of the author's earlier book, Algebraic Topology; an Introduction (GTM 56) together with almost all of his book, Singular Homology Theory (GTM 70). The material from the two earlier books has been substantially revised, corrected, and brought up to date.

Two-Dimensional Random Walk

Author : Serguei Popov
Publisher : Cambridge University Press
ISBN 13 : 1108472451
Total Pages : 224 pages
Book Rating : 4.1/5 (84 download)

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Book Synopsis Two-Dimensional Random Walk by : Serguei Popov

Download or read book Two-Dimensional Random Walk written by Serguei Popov and published by Cambridge University Press. This book was released on 2021-03-18 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: A visual, intuitive introduction in the form of a tour with side-quests, using direct probabilistic insight rather than technical tools.

Chaotic Dynamics in Two-dimensional Noninvertible Maps

Author : C. Mira
Publisher : World Scientific
ISBN 13 : 9789810216474
Total Pages : 638 pages
Book Rating : 4.2/5 (164 download)

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Book Synopsis Chaotic Dynamics in Two-dimensional Noninvertible Maps by : C. Mira

Download or read book Chaotic Dynamics in Two-dimensional Noninvertible Maps written by C. Mira and published by World Scientific. This book was released on 1996 with total page 638 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is essentially devoted to complex properties (Phase plane structure and bifurcations) of two-dimensional noninvertible maps, i.e. maps having either a non-unique inverse, or no real inverse, according to the plane point. They constitute models of sets of discrete dynamical systems encountered in Engineering (Control, Signal Processing, Electronics), Physics, Economics, Life Sciences. Compared to the studies made in the one-dimensional case, the two-dimensional situation remained a long time in an underdeveloped state. It is only since these last years that the interest for this research has increased. Therefore the book purpose is to give a global presentation of a matter, available till now only in a partial form. Fundamental notions and tools (such as “critical manifolds”), as the most part of results, are accompanied by many examples and figures.