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Noua corpora regularia: seu, Quinque corporum regularium simplicium, in quinque alia regularia composita, metamorphosis. Inventa ante annos 60 à Thoma Diggseio Armigero, jam, prolematibus additis nonnullis, demonstrata à nepote
Authors: --- --- --- --- --- et al.
Year: 1634 Publisher: Londini : Apud Thomam Harperum,

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N-gons
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ISBN: 1442656441 9781442656444 Year: 1975 Publisher: Toronto, [Ontario] ; Buffalo, [New York] : University of Toronto Press,

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This book, a translation of the German volume n-Ecke, 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 n-gons. The twelve chapters treat n-gons, classes of n-gons, and mapping of the set of n-gons 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)

Hyperbolic Functions : with Configuration Theorems and Equivalent and Equidecomposable Figures
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ISBN: 0486170055 0486458865 Year: 2013 Publisher: Newburyport : Dover Publications,

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This single-volume 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


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An adventure in multidimensional space : the art and geometry of polygons, polyhedra, and polytopes
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ISBN: 0471816485 Year: 1986 Publisher: New York (N.Y.): Wiley


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Islamic Geometric Patterns : Their Historical Development and Traditional Methods of Construction
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ISBN: 1441902171 1441902163 Year: 2017 Publisher: New York, NY : Springer New York : Imprint: Springer,

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The main focus of this unique book is an in-depth 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 all-but-lost 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 al-Masjid al-Haram (Grand Mosque) in Mecca, and the al-Masjid 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.


Book
Serious Fun with Flexagons : A Compendium and Guide
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ISBN: 9400736800 9048125022 9786612655609 1282655604 9048125030 Year: 2009 Publisher: Dordrecht : Springer Netherlands : Imprint: Springer,

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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. .


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Polygons, Polyominoes and Polycubes
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ISBN: 1402099266 1402099274 Year: 2009 Publisher: Dordrecht : Springer Netherlands : Imprint: Springer,

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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 bio-informatics – 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 two-dimensions, 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.

Algorithms for parallel polygon rendering
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ISBN: 3540513949 354046204X Year: 1989 Volume: vol 373 Publisher: Berlin Springer

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This book is the result of the research in the implementation of polygon-based graphics operations on certain general purpose parallel processors; the aim is to provide a speed-up 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 dual-paradigm (SIMD-MIMD) machine constructed out of a DAP-like 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.

Keywords

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 --- Three-dimensional graphics and realism: animation; visible line/surface algorithms (Computer graphics) --- Digital techniques --- 681.3*I37 Three-dimensional 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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