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eebo0018
Polygons  Geometry  Polygonal figures  Geometry, Plane  Shapes  Mathematics, Greek
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This book, a translation of the German volume nEcke, presents an elegant geometric theory which, starting from quite elementary geometrical observations, exhibits an interesting connection between geometry and fundamental ideas of modern algebra in a form that is easily accessible to the student who lacks a sophisticated background in mathematics. It stimulates geometrical thought by applying the tools of linear algebra and the algebra of polynomials to a concrete geometrical situation to reveal some rather surprising insights into the geometry of ngons. The twelve chapters treat ngons, classes of ngons, and mapping of the set of ngons into itself. Exercises are included throughout, and two appendixes, by Henner Kinder and Eckart Schmidt, provide background material on lattices and cyclotomic polynomials.(Mathematical Expositions No. 18)
Polygons.  Set theory.  Aggregates  Classes (Mathematics)  Ensembles (Mathematics)  Mathematical sets  Sets (Mathematics)  Theory of sets  Logic, Symbolic and mathematical  Mathematics  Polygonal figures  Geometry, Plane  Shapes
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This singlevolume compilation of three books centers on Hyperbolic Functions, an introduction to the relationship between the hyperbolic sine, cosine, and tangent, and the geometric properties of the hyperbola. The development of the hyperbolic functions, in addition to those of the trigonometric (circular) functions, appears in parallel columns for comparison. A concluding chapter introduces natural logarithms and presents analytic expressions for the hyperbolic functions.The second book, Configuration Theorems, requires only the most elementary background in plane and solid geometry. It dis
Exponential functions  Geometry, Projective  Polygons  Polyhedra  Mathematics  Physical Sciences & Mathematics  Calculus  Polyhedral figures  Polyhedrons  Geometry, Solid  Shapes  Polygonal figures  Geometry, Plane  Projective geometry  Geometry, Modern  Functions, Exponential  Hyperbolic functions  Exponents (Algebra)  Logarithms  Transcendental functions
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Visual perception  Space (Art)  Form (Aesthetics)  Polygons  Polyhedra  Polytopes  Perception visuelle  Espace (Art)  Forme (Esthétique)  Polygones  Polyèdres  Visual Perception  514.1  Optics, Psychological  Vision  Perception  Visual discrimination  Art  Hyperspace  Topology  Polyhedral figures  Polyhedrons  Geometry, Solid  Shapes  Polygonal figures  Geometry, Plane  Aesthetic form  Aesthetics  General geometry  Psychological aspects  514.1 General geometry  Forme (Esthétique)  Polyèdres  Negative space (Art)
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The main focus of this unique book is an indepth examination of the polygonal technique; the primary method used by master artists of the past in creating Islamic geometric patterns. The author details the design methodology responsible for this allbutlost art form and presents evidence for its use from the historical record, both of which are vital contributions to the understanding of this ornamental tradition. Additionally, the author examines the historical development of Islamic geometric patterns, the significance of geometric design within the broader context of Islamic ornament as a whole, the formative role that geometry plays throughout the Islamic ornamental arts (including calligraphy, the floral idiom, dome decoration, geometric patterns, and more), and the underexamined question of pattern classification. Featuring over 600 beautiful color images, Islamic Geometric Patterns: Their Historical Development and Traditional Methods of Construction is a valuable addition to the literature of Islamic art, architecture and geometric patterns. This book is ideal for students and scholars of geometry, the history of mathematics, and the history of Islamic art, architecture, and culture. In addition, artists, designers, craftspeople, and architects will all find this book an exceptionally informative and useful asset in their fields. Jay Bonner is an architectural ornamentalist and unaffiliated scholar of Islamic geometric design. He received his MDes from the Royal College of Art in London (1983). He has contributed ornamental designs for many international architectural projects, including the expansion of both the alMasjid alHaram (Grand Mosque) in Mecca, and the alMasjid an Nawabi (Prophet’s Mosque) in Medina, as well the Tomb of Sheikh Hujwiri in Lahore, and the Ismaili Centre in London – to name but a few. He is committed to the revitalization of Islamic geometric design through the teaching of tradi tional methodological practices. To this end, in addition to publishing, Jay Bonner has lectured and taught design seminars at many universities and conferences in North America, Europe, North Africa and Asia.
Geometry in art.  Polygons.  Polygonal figures  Mathematics.  Architecture.  Geometry.  History.  History of Mathematical Sciences.  Architectural History and Theory.  Geometry, Plane  Shapes  Mathematics  Euclid's Elements  Architecture, Western (Western countries)  Building design  Buildings  Construction  Western architecture (Western countries)  Art  Building  Design and construction  Annals  Auxiliary sciences of history  Math  Science
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A flexagon is a motion structure that has the appearance of a ring of hinged polygons. It can be flexed to display different pairs of faces, usually in cyclic order. Flexagons can be appreciated as toys or puzzles, as a recreational mathematics topic, and as the subject of serious mathematical study. Workable paper models of flexagons are easy to make and entertaining to manipulate. The mathematics of flexagons is complex, and how a flexagon works is not immediately obvious on examination of a paper model. Recent geometric analysis, included in the book, has improved theoretical understanding of flexagons, especially relationships between different types. This profusely illustrated book is arranged in a logical order appropriate for a textbook on the geometry of flexagons. It is written so that it can be enjoyed at both the recreational mathematics level, and at the serious mathematics level. The only prerequisite is some knowledge of elementary geometry, including properties of polygons. A feature of the book is a compendium of over 100 nets for making paper models of some of the more interesting flexagons, chosen to complement the text. These are accurately drawn and reproduced at half full size. Many of the nets have not previously been published. Instructions for assembling and manipulating the flexagons are included. .
Geometry, Solid Models.  Mathematical recreations.  Paper work.  Polygons Models.  Polyhedra Models.  Geometry, Solid  Polygons  Polyhedra  Paper work  Mathematical recreations  Mathematics  Physical Sciences & Mathematics  Geometry  Models  Mathematical puzzles  Number games  Recreational mathematics  Recreations, Mathematical  Paper craft  Papercutting  Paper folding (Handicraft)  Papercraft  Polygonal figures  Solid geometry  Mathematics.  Geometry.  History.  Engineering.  Engineering, general.  Mathematics, general.  History of Mathematical Sciences.  Models.  Puzzles  Scientific recreations  Games in mathematics education  Magic squares  Magic tricks in mathematics education  Geometrical models  Math  Science  Construction  Industrial arts  Technology  Euclid's Elements  Annals  Auxiliary sciences of history
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This unique book gives a comprehensive account of new mathematical tools used to solve polygon problems. In the 20th and 21st centuries, many problems in mathematics, theoretical physics and theoretical chemistry – and more recently in molecular biology and bioinformatics – can be expressed as counting problems, in which specified graphs, or shapes, are counted. One very special class of shapes is that of polygons. These are closed, connected paths in space. We usually sketch them in twodimensions, but they can exist in any dimension. The typical questions asked include "how many are there of a given perimeter?", "how big is the average polygon of given perimeter?", and corresponding questions about the area or volume enclosed. That is to say "how many enclosing a given area?" and "how large is an average polygon of given area?" Simple though these questions are to pose, they are extraordinarily difficult to answer. They are important questions because of the application of polygon, and the related problems of polyomino and polycube counting, to phenomena occurring in the natural world, and also because the study of these problems has been responsible for the development of powerful new techniques in mathematics and mathematical physics, as well as in computer science. These new techniques then find application more broadly. The book brings together chapters from many of the major contributors in the field. An introductory chapter giving the history of the problem is followed by fourteen further chapters describing particular aspects of the problem, and applications to biology, to surface phenomena and to computer enumeration methods.
Polygons  Polyominoes  Physics  General  Geometry  Physics  Mathematics  Physical Sciences & Mathematics  Polygons.  Polyominoes.  Polygonal figures  Physics.  Chemometrics.  Numerical analysis.  Algorithms.  Combinatorics.  Statistical physics.  Dynamical systems.  Mathematical Methods in Physics.  Numeric Computing.  Statistical Physics, Dynamical Systems and Complexity.  Math. Applications in Chemistry.  Combinatorial designs and configurations  Geometry, Plane  Shapes  Mathematical physics.  Electronic data processing.  Chemistry  Complex Systems.  Mathematics.  Combinatorics  Algebra  Mathematical analysis  Algorism  Arithmetic  Physical mathematics  ADP (Data processing)  Automatic data processing  Data processing  EDP (Data processing)  IDP (Data processing)  Integrated data processing  Computers  Office practice  Foundations  Automation  Chemistry, Analytic  Analytical chemistry  Dynamical systems  Kinetics  Mechanics, Analytic  Force and energy  Mechanics  Statics  Mathematical statistics  Natural philosophy  Philosophy, Natural  Physical sciences  Dynamics  Measurement  Statistical methods
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This book is the result of the research in the implementation of polygonbased graphics operations on certain general purpose parallel processors; the aim is to provide a speedup over sequential implementations of the graphics operations concerned, and the resulting software can be viewed as a subset of the application suites of the relevant parallel machines. A literature review and a brief description of the architectures considered give an introduction into the field. Most algorithms are consistently presented in an informally defined extension of the Occam language which includes Single Instruction Multiple Data stream (SIMD) data types and operations on them. Original methods for polygon rendering  including the operations of filling, hidden surface elimination and smooth shading  are presented for SIMD architectures like the DAP and for a dualparadigm (SIMDMIMD) machine constructed out of a DAPlike processor array and a transputer network. Polygon clipping algorithms for both transputer and the DAP are described and contrasted. Apart from the information presented in the book and the useful literature survey, the reader can also expect to gain an insight into the programming of the relevant parallel machines.
Artificial intelligence. Robotics. Simulation. Graphics  Computer architecture. Operating systems  Computer algorithms  Computer graphics  Parallel processing (Electronic computers)  Polygons  681.3*C12  681.3*I37  Polygonal figures  Geometry, Plane  Shapes  High performance computing  Multiprocessors  Parallel programming (Computer science)  Supercomputers  Automatic drafting  Graphic data processing  Graphics, Computer  Computer art  Graphic arts  Electronic data processing  Engineering graphics  Image processing  Algorithms  Multiple data stream architectures (multiprocessors): MIMD; SIMD; pipeline and parallel processors; array, vector, associative processors; interconnection architectures: common bus, multiport memory, crossbar switch  Threedimensional graphics and realism: animation; visible line/surface algorithms (Computer graphics)  Digital techniques  681.3*I37 Threedimensional graphics and realism: animation; visible line/surface algorithms (Computer graphics)  681.3*C12 Multiple data stream architectures (multiprocessors): MIMD; SIMD; pipeline and parallel processors; array, vector, associative processors; interconnection architectures: common bus, multiport memory, crossbar switch  Computer network architectures.  Computer graphics.  Computer science.  Computer System Implementation.  Computer Graphics.  Processor Architectures.  Programming Languages, Compilers, Interpreters.  Informatics  Science  Architectures, Computer network  Network architectures, Computer  Computer architecture
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