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Non Euclidean Laguerre Geometry And Incircular Nets
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Book Synopsis Non-Euclidean Laguerre Geometry and Incircular Nets by : Alexander I. Bobenko
Download or read book Non-Euclidean Laguerre Geometry and Incircular Nets written by Alexander I. Bobenko and published by Springer Nature. This book was released on 2021-10-29 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is a comprehensive and yet accessible introduction to non-Euclidean Laguerre geometry, for which there exists no previous systematic presentation in the literature. Moreover, we present new results by demonstrating all essential features of Laguerre geometry on the example of checkerboard incircular nets. Classical (Euclidean) Laguerre geometry studies oriented hyperplanes, oriented hyperspheres, and their oriented contact in Euclidean space. We describe how this can be generalized to arbitrary Cayley-Klein spaces, in particular hyperbolic and elliptic space, and study the corresponding groups of Laguerre transformations. We give an introduction to Lie geometry and describe how these Laguerre geometries can be obtained as subgeometries. As an application of two-dimensional Lie and Laguerre geometry we study the properties of checkerboard incircular nets.
Book Synopsis Euclidean and Non Euclidean Geometry by :
Download or read book Euclidean and Non Euclidean Geometry written by and published by . This book was released on 1986 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Non-Euclidean Geometry by : Open University M203/Geometry Block
Download or read book Non-Euclidean Geometry written by Open University M203/Geometry Block and published by . This book was released on 1995 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Elements of Non-Euclidean Geometry by : Julian Lowell Coolidge
Download or read book The Elements of Non-Euclidean Geometry written by Julian Lowell Coolidge and published by Createspace Independent Publishing Platform. This book was released on 2017-07-08 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Elements of Non-Euclidean Geometry by Julian Lowell Coolidge Ph.D. - Harvard University Contents: CHAPTER I FOUNDATION FOR METRICAL GEOMETRY IN A LIMITED REGION Fundamental assumptions and definitions Sums and differences of distances Serial arrangement of points on a line Simple descriptive properties of plane and space CHAPTER II CONGRUENT TRANSFORMATIONS Axiom of continuity Division of distances Measure of distance Axiom of congruent transformations Definition of angles, their properties Comparison of triangles Side of a triangle not greater than sum of other two Comparison and measurement of angles Nature of the congruent group Definition of dihedral angles, their properties CHAPTER III THE THREE HYPOTHESES A variable angle is a continuous function of a variable distance Saccheri's theorem for isosceles birectangular quadrilaterals The existence of one rectangle implies the existence of an infinite number Three assumptions as to the sum of the angles of a right triangle Three assumptions as to the sum of the angles of any triangle, their categorical nature Definition of the euclidean, hyperbolic, and elliptic hypotheses Geometry in the infinitesimal domain obeys the euclidean hypothesis CHAPTER IV THE INTRODUCTION OF TRIGONOMETRIC FORMULAE Limit of ratio of opposite sides of diminishing isosceles quadrilateral Continuity of the resulting function Its functional equation and solution Functional equation for the cosine of an angle Non-euclidean form for the pythagorean theorem Trigonometric formulae for right and oblique triangles CHAPTER V ANALYTIC FORMULAE Directed distances Group of translations of a line Positive and negative directed distances Coordinates of a point on a line Coordinates of a point in a plane Finite and infinitesimal distance formulae, the non-euclidean plane as a surface of constant Gaussian curvature Equation connecting direction cosines of a line Coordinates of a point in space Congruent transformations and orthogonal substitutions Fundamental formulae for distance and angle CHAPTER VI CONSISTENCY AND SIGNIFICANCE OF THE AXIOMS Examples of geometries satisfying the assumptions made Relative independence of the axioms CHAPTER VII THE GEOMETRIC AND ANALYTIC EXTENSION OF SPACE Possibility of extending a segment by a definite amount in the euclidean and hyperbolic cases Euclidean and hyperbolic space Contradiction arising under the elliptic hypothesis New assumptions identical with the old for limited region, but permitting the extension of every segment by a definite amount Last axiom, free mobility of the whole system One to one correspondence of point and coordinate set in euclidean and hyperbolic cases Ambiguity in the elliptic case giving rise to elliptic and spherical geometry Ideal elements, extension of all spaces to be real continua Imaginary elements geometrically defined, extension of all spaces to be perfect continua in the complex domain Cayleyan Absolute, new form for the definition of distance Extension of the distance concept to the complex domain Case where a straight line gives a maximum distance CHAPTER VIII THE GROUPS OF CONGRUENT TRANSFORMATIONS Congruent transformations of the straight line ,, ,, ,, hyperbolic plane ,, ,, ,, elliptic plane ,, ,, ,, euclidean plane ,, ,, ,, hyperbolic space ,, ,, ,, elliptic and spherical space Clifford parallels, or paratactic lines CHAPTER IX POINT, LINE, AND PLANE TREATED ANALYTICALLY CHAPTER X THE HIGHER LINE GEOMETRY CHAPTER XI THE CIRCLE AND THE SPHERE CHAPTER XII CONIC SECTIONS CHAPTER XIII QUADRIC SURFACES CHAPTER XIV AREAS AND VOLUMES Volume of a cone of revolution, a sphere, the whole of elliptic or of spherical space CHAPTER XV INTRODUCTION TO DIFFERENTIAL GEOMETRY CHAPTER XVI DIFFERENTIAL LINE-GEOMETRY CHAPTER XVII MULTIPLY CONNECTED SPACES CHAPTER XVIII THE PROJECTIVE BASIS OF NON-EUCLIDEAN GEOMETRY CHAPTER XIX THE DIFFERENTIAL BASIS FOR EUCLIDEAN AND NON-EUCLIDEAN GEOMETRY
Download or read book Non-Euclidean Geometry written by and published by . This book was released on 1963 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Non-Euclidean Geometry by : Adelheit Steeneck
Download or read book Non-Euclidean Geometry written by Adelheit Steeneck and published by . This book was released on 1920 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Euclidean and Non-Euclidean Geometry International Student Edition by : Patrick J. Ryan
Download or read book Euclidean and Non-Euclidean Geometry International Student Edition written by Patrick J. Ryan and published by Cambridge University Press. This book was released on 2009-09-04 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a rigorous treatment of the fundamentals of plane geometry: Euclidean, spherical, elliptical and hyperbolic.
Book Synopsis Non-Euclidean Geometry by : Roberto Bonola
Download or read book Non-Euclidean Geometry written by Roberto Bonola and published by . This book was released on 1912 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Examines various attempts to prove Euclid's parallel postulate -- by the Greeks, Arabs and Renaissance mathematicians. Ranging through the 17th, 18th, and 19th centuries, it considers forerunners and founders such as Saccheri, Lambert, Legendre, W. Bolyai, Gauss, Schweikart, Taurinus, J. Bolyai and Lobachewsky.
Book Synopsis Non-Euclidean Geometry by : Henry Parker Manning
Download or read book Non-Euclidean Geometry written by Henry Parker Manning and published by . This book was released on 1901 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Computational Approach to Riemann Surfaces by : Alexander I. Bobenko
Download or read book Computational Approach to Riemann Surfaces written by Alexander I. Bobenko and published by Springer Science & Business Media. This book was released on 2011-02-12 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume offers a well-structured overview of existent computational approaches to Riemann surfaces and those currently in development. The authors of the contributions represent the groups providing publically available numerical codes in this field. Thus this volume illustrates which software tools are available and how they can be used in practice. In addition examples for solutions to partial differential equations and in surface theory are presented. The intended audience of this book is twofold. It can be used as a textbook for a graduate course in numerics of Riemann surfaces, in which case the standard undergraduate background, i.e., calculus and linear algebra, is required. In particular, no knowledge of the theory of Riemann surfaces is expected; the necessary background in this theory is contained in the Introduction chapter. At the same time, this book is also intended for specialists in geometry and mathematical physics applying the theory of Riemann surfaces in their research. It is the first book on numerics of Riemann surfaces that reflects the progress made in this field during the last decade, and it contains original results. There are a growing number of applications that involve the evaluation of concrete characteristics of models analytically described in terms of Riemann surfaces. Many problem settings and computations in this volume are motivated by such concrete applications in geometry and mathematical physics.
Book Synopsis Discrete Differential Geometry by : Alexander I. Bobenko
Download or read book Discrete Differential Geometry written by Alexander I. Bobenko and published by American Mathematical Society. This book was released on 2023-09-14 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: An emerging field of discrete differential geometry aims at the development of discrete equivalents of notions and methods of classical differential geometry. The latter appears as a limit of a refinement of the discretization. Current interest in discrete differential geometry derives not only from its importance in pure mathematics but also from its applications in computer graphics, theoretical physics, architecture, and numerics. Rather unexpectedly, the very basic structures of discrete differential geometry turn out to be related to the theory of integrable systems. One of the main goals of this book is to reveal this integrable structure of discrete differential geometry. For a given smooth geometry one can suggest many different discretizations. Which one is the best? This book answers this question by providing fundamental discretization principles and applying them to numerous concrete problems. It turns out that intelligent theoretical discretizations are distinguished also by their good performance in applications. The intended audience of this book is threefold. It is a textbook on discrete differential geometry and integrable systems suitable for a one semester graduate course. On the other hand, it is addressed to specialists in geometry and mathematical physics. It reflects the recent progress in discrete differential geometry and contains many original results. The third group of readers at which this book is targeted is formed by specialists in geometry processing, computer graphics, architectural design, numerical simulations, and animation. They may find here answers to the question “How do we discretize differential geometry?” arising in their specific field. Prerequisites for reading this book include standard undergraduate background (calculus and linear algebra). No knowledge of differential geometry is expected, although some familiarity with curves and surfaces can be helpful.
Book Synopsis Poncelet Porisms and Beyond by : Vladimir Dragović
Download or read book Poncelet Porisms and Beyond written by Vladimir Dragović and published by Springer Science & Business Media. This book was released on 2011-05-02 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of the book is to present, in a complete and comprehensive way, areas of current research interlacing around the Poncelet porism: dynamics of integrable billiards, algebraic geometry of hyperelliptic Jacobians, and classical projective geometry of pencils of quadrics. The most important results and ideas, classical as well as modern, connected to the Poncelet theorem are presented, together with a historical overview analyzing the classical ideas and their natural generalizations. Special attention is paid to the realization of the Griffiths and Harris programme about Poncelet-type problems and addition theorems. This programme, formulated three decades ago, is aimed to understanding the higher-dimensional analogues of Poncelet problems and the realization of the synthetic approach of higher genus addition theorems.
Book Synopsis Spatial Tessellations by : Atsuyuki Okabe
Download or read book Spatial Tessellations written by Atsuyuki Okabe and published by John Wiley & Sons. This book was released on 2009-09-25 with total page 696 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spatial data analysis is a fast growing area and Voronoi diagrams provide a means of naturally partitioning space into subregions to facilitate spatial data manipulation, modelling of spatial structures, pattern recognition and locational optimization. With such versatility, the Voronoi diagram and its relative, the Delaunay triangulation, provide valuable tools for the analysis of spatial data. This is a rapidly growing research area and in this fully updated second edition the authors provide an up-to-date and comprehensive unification of all the previous literature on the subject of Voronoi diagrams. Features: * Expands on the highly acclaimed first edition * Provides an up-to-date and comprehensive survey of the existing literature on Voronoi diagrams * Includes a useful compendium of applications * Contains an extensive bibliography A wide range of applications is discussed, enabling this book to serve as an important reference volume on this topic. The text will appeal to students and researchers studying spatial data in a number of areas, in particular, applied probability, computational geometry, and Geographic Information Science (GIS). This book will appeal equally to those whose interests in Voronoi diagrams are theoretical, practical or both.
Book Synopsis A Concise Handbook of Mathematics, Physics, and Engineering Sciences by : Andrei D. Polyanin
Download or read book A Concise Handbook of Mathematics, Physics, and Engineering Sciences written by Andrei D. Polyanin and published by CRC Press. This book was released on 2010-10-18 with total page 1080 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Concise Handbook of Mathematics, Physics, and Engineering Sciences takes a practical approach to the basic notions, formulas, equations, problems, theorems, methods, and laws that most frequently occur in scientific and engineering applications and university education. The authors pay special attention to issues that many engineers and students
Book Synopsis Computational Line Geometry by : Helmut Pottmann
Download or read book Computational Line Geometry written by Helmut Pottmann and published by Springer Science & Business Media. This book was released on 2009-12-16 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: " A unique and fascinating blend, which is shown to be useful for a variety of applications, including robotics, geometrical optics, computer animation, and geometric design. The contents of the book are visualized by a wealth of carefully chosen illustrations, making the book a shear pleasure to read, or even to just browse in." Mathematical Reviews
Book Synopsis Guide to Essential Math by : Sy M. Blinder
Download or read book Guide to Essential Math written by Sy M. Blinder and published by Newnes. This book was released on 2013-02-14 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reminds students in junior, senior and graduate level courses in physics, chemistry and engineering of the math they may have forgotten (or learned imperfectly) that is needed to succeed in science courses. The focus is on math actually used in physics, chemistry, and engineering, and the approach to mathematics begins with 12 examples of increasing complexity, designed to hone the student's ability to think in mathematical terms and to apply quantitative methods to scientific problems. Detailed illustrations and links to reference material online help further comprehension. The second edition features new problems and illustrations and features expanded chapters on matrix algebra and differential equations. Use of proven pedagogical techniques developed during the author’s 40 years of teaching experience New practice problems and exercises to enhance comprehension Coverage of fairly advanced topics, including vector and matrix algebra, partial differential equations, special functions and complex variables
Book Synopsis Architectural Geometry by : Helmut Pottmann
Download or read book Architectural Geometry written by Helmut Pottmann and published by . This book was released on 2007 with total page 752 pages. Available in PDF, EPUB and Kindle. Book excerpt: Architectural Geometry is the first book to introduce a revolutionary new approach to design. Geometry lies at the core of the architectural design process. It is omnipresent, from the initial form-finding stages to the actual construction. Modern constructive geometry provides a variety of tools for the efficient design, analysis, and manufacture of complex shapes. This results in new challenges for architecture. However, the architectural application also poses new problems to geometry. Architectural geometry is therefore an entire research area, currently emerging at the border between applied geometry and architecture. Written for students, architects, construction engineers, and industrial designers – Architectural Geometry is a source of inspiration for scientists interested in applications of geometry processing in architecture and art. With over 700 pages, including 2,100 full-color images of built architecture, architectural projects, and artwork, Architectural Geometry takes readers from basic to advanced geometry then leads them to the cutting-edge of research in the architectural geometry field.
