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Spreads Of Three Dimensional And Five Dimensional Finite Projective Geometries
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Book Synopsis Spreads of Three-dimensional and Five-dimensional Finite Projective Geometries by :
Download or read book Spreads of Three-dimensional and Five-dimensional Finite Projective Geometries written by and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis is primarily concerned with specific types of spreads of three-dimensional and five-dimensional projective geometries over finite fields. Spreads are a partition of a projective geometry, and are used to construct translation planes through the Andre/Bruck-Bose construction. This thesis uses the Bruck-Bose model, which is more geometric in nature. The types of spreads examined include the following: spreads of five-dimensional projective geometries for three-dimensional flag-transitive affine planes, polarity-paired spreads of three-dimensional projective geometries, and spreads of five-dimensional projective geometries constructed from a three-dimensional circle geometry. In the introduction to the thesis, a short historical account is given of some aspects of modern incidence geometry. Specifically, a partial history of the theory of projective and affine planes that leads to the study of translation planes. In Chapters Two and Three the definitions of a projective plane and translation plane are given, along with properties of these objects that will be useful in their study. Also the classical (Desarguesian) projective plane and the classical projective geometries are defined. It is these higher-dimensional Desarguesian geometries that are needed for the Bruck-Bose model of translation planes. The Andre/Bruck-Bose construction is explained in Chapter Four. This includes a discussion of the Miquelian inversive plane, which can be used to model a fundamental family of spreads called "regular". In Chapter Five spreads of five-dimensional projective geometries are used to construct odd order three-dimensional flag-transitive affine planes. This involves examining the way that planes in the spread intersect a partition of a five-dimensional geometry. Chapter Six is concerned with polarities of three-dimensional geometries applied to spreads of that geometry, leading to the concept of polarity-paired spreads. The symplectic polarity-paired spreads are used to construct a certain class of ovoids of a specific generalized quadrangle. In Chapter Seven a three-dimensional circle geometry is used to construct spreads of five-dimensional projective geometries. This circle geometry and spreads constructed from a regular spread mirror the concept of the Miquelian inversive plane and its relationship to subregular spreads from a regular spread of a three-dimensional projective geometry. Finally, the possibility of further work is discussed in Chapter Eight.
Book Synopsis Geometry In Our Three-dimensional World by : Alfred S Posamentier
Download or read book Geometry In Our Three-dimensional World written by Alfred S Posamentier and published by World Scientific. This book was released on 2021-11-24 with total page 441 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents a comprehensive overview of various aspects of three-dimensional geometry that can be experienced on a daily basis. By covering the wide range of topics — from the psychology of spatial perception to the principles of 3D modelling and printing, from the invention of perspective by Renaissance artists to the art of Origami, from polyhedral shapes to the theory of knots, from patterns in space to the problem of optimal packing, and from the problems of cartography to the geometry of solar and lunar eclipses — this book provides deep insight into phenomena related to the geometry of space and exposes incredible nuances that can enrich our lives.The book is aimed at the general readership and provides more than 420 color illustrations that support the explanations and replace formal mathematical arguments with clear graphical representations.
Book Synopsis Finite Geometries by : Peter Dembowski
Download or read book Finite Geometries written by Peter Dembowski and published by Springer Science & Business Media. This book was released on 1997 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: Peter Dembowski was born in Berlin on April 1, 1928. After studying mathematics at the University of Frankfurt of Main, he pursued his graduate studies at Brown Unviersity and the University of Illinois, mainly with R. Baer. Dembowski returned to Frankfurt in 1956. Shortly before his premature death in January 1971, he had been appointed to a chair at the University of Tuebingen. Dembowski taught at the universities of Frankfurt and Tuebingen and - as visiting Professor - in London (Queen Mary College), Rome, and Madison, WI. Dembowski's chief research interest lay in the connections between finite geometries and group theory. His book "Finite Geometries" brought together essentially all that was known at that time about finite geometrical structures, including key results of the author, in a unified and structured perspective. This book became a standard reference as soon as it appeared in 1968. It influenced the expansion of combinatorial geometric research, and left its trace also in neighbouring areas.
Book Synopsis Projective Geometry by : Albrecht Beutelspacher
Download or read book Projective Geometry written by Albrecht Beutelspacher and published by Cambridge University Press. This book was released on 1998-01-29 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Projective geometry is not only a jewel of mathematics, but has also many applications in modern information and communication science. This book presents the foundations of classical projective and affine geometry as well as its important applications in coding theory and cryptography. It also could serve as a first acquaintance with diagram geometry. Written in clear and contemporary language with an entertaining style and around 200 exercises, examples and hints, this book is ideally suited to be used as a textbook for study in the classroom or on its own.
Book Synopsis The Shape of Space by : Jeffrey R. Weeks
Download or read book The Shape of Space written by Jeffrey R. Weeks and published by Marcel Dekker. This book was released on 1985 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Shape of Space brings topology to the general reader by showing how to visualize manifolds directly ... complements existing textbooks, which often deal only in abstractions, by offering a wealth of concrete examples ... includes the first elementary exposition of William P. Thurston's revolutionary discoveries ... applies topology to cosmology ... gives the first simple pictorial exposition of the Gauss-Bonnet formula ... builds intuition with more than 140 hands-on exercises, all with complete solutions ... and offers over 170 illustrations. An annotated bibliography lists useful references for further study on specific topics.
Book Synopsis Spreads in Three-dimensional Projective Space by : David John Oakden
Download or read book Spreads in Three-dimensional Projective Space written by David John Oakden and published by . This book was released on 1973 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Foundations of Three-Dimensional Euclidean Geometry by : Izu Vaisman
Download or read book Foundations of Three-Dimensional Euclidean Geometry written by Izu Vaisman and published by CRC Press. This book was released on 2020-11-26 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents to the reader a modern axiomatic construction of three-dimensional Euclidean geometry in a rigorous and accessible form. It is helpful for high school teachers who are interested in the modernization of the teaching of geometry.
Book Synopsis Bulletin of the American Mathematical Society by : American Mathematical Society
Download or read book Bulletin of the American Mathematical Society written by American Mathematical Society and published by . This book was released on 1912 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Combinatorics '90 written by A. Barlotti and published by Elsevier. This book was released on 1992-08-17 with total page 577 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume forms a valuable source of information on recent developments in research in combinatorics, with special regard to the geometric point of view. Topics covered include: finite geometries (arcs, caps, special varieties in a Galois space; generalized quadrangles; Benz planes; foundation of geometry), partial geometries, Buekenhout geometries, transitive permutation sets, flat-transitive geometries, design theory, finite groups, near-rings and semifields, MV-algebras, coding theory, cryptography and graph theory in its geometric and design aspects.
Book Synopsis Mostly Finite Geometries by : Norman Johnson
Download or read book Mostly Finite Geometries written by Norman Johnson and published by CRC Press. This book was released on 1997-05-06 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on the proceedings of the conference held at the University of Iowa, in honour and celebration of the mathematician T.G. Ostrom's 80th birthday, this text focuses on finite geometries as well as topological geometries in the infinite case, some of which originate with ideas of finite geometric objects. It includes information about flocks of quadratic cones and related geometric and combinatorial structures.
Book Synopsis Bulletin (new Series) of the American Mathematical Society by :
Download or read book Bulletin (new Series) of the American Mathematical Society written by and published by . This book was released on 1912 with total page 558 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Finite Geometries by : Catherine Anne Baker
Download or read book Finite Geometries written by Catherine Anne Baker and published by CRC Press. This book was released on 2020-10-14 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a compilation of the papers presented at the conference in Winnipeg on the subject of finite geometry in 1984. It covers different fields in finite geometry: classical finite geometry, the geometry of finite planes, geometric structures and the theory of translation planes.
Book Synopsis Finite Geometries by : Aart Blokhuis
Download or read book Finite Geometries written by Aart Blokhuis and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: When? These are the proceedings of Finite Geometries, the Fourth Isle of Thorns Conference, which took place from Sunday 16 to Friday 21 July, 2000. It was organised by the editors of this volume. The Third Conference in 1990 was published as Advances in Finite Geometries and Designs by Oxford University Press and the Second Conference in 1980 was published as Finite Geometries and Designs by Cambridge University Press. The main speakers were A. R. Calderbank, P. J. Cameron, C. E. Praeger, B. Schmidt, H. Van Maldeghem. There were 64 participants and 42 contributions, all listed at the end of the volume. Conference web site http://www. maths. susx. ac. uk/Staff/JWPH/ Why? This collection of 21 articles describes the latest research and current state of the art in the following inter-linked areas: • combinatorial structures in finite projective and affine spaces, also known as Galois geometries, in which combinatorial objects such as blocking sets, spreads and partial spreads, ovoids, arcs and caps, as well as curves and hypersurfaces, are all of interest; • geometric and algebraic coding theory; • finite groups and incidence geometries, as in polar spaces, gener alized polygons and diagram geometries; • algebraic and geometric design theory, in particular designs which have interesting symmetric properties and difference sets, which play an important role, because of their close connections to both Galois geometry and coding theory.
Book Synopsis Finite Geometries by : Catherine Anne Baker
Download or read book Finite Geometries written by Catherine Anne Baker and published by CRC Press. This book was released on 2020-10-15 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a compilation of the papers presented at the conference in Winnipeg on the subject of finite geometry in 1984. It covers different fields in finite geometry: classical finite geometry, the geometry of finite planes, geometric structures and the theory of translation planes.
Book Synopsis Spreads in Three-dimensional Projective Space by : David John Oakden
Download or read book Spreads in Three-dimensional Projective Space written by David John Oakden and published by . This book was released on 1973 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Finite Fields and Applications by : Stephen Cohen
Download or read book Finite Fields and Applications written by Stephen Cohen and published by Cambridge University Press. This book was released on 1996-09-28 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite fields are algebraic structures in which there is much research interest. This book gives a state-of-the-art account of finite fields and their applications in communications (coding theory, cryptology), combinatorics, design theory, quasirandom points, algorithms and their complexity. Typically, theory and application are tightly interwoven in the survey articles and original research papers included here. The book also demonstrates interconnections with other branches of pure mathematics such as number theory, group theory and algebraic geometry. This volume is an invaluable resource for any researcher in finite fields or related areas.
Book Synopsis Theory and Applications of Finite Fields by : Michel Lavrauw
Download or read book Theory and Applications of Finite Fields written by Michel Lavrauw and published by American Mathematical Soc.. This book was released on 2012 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the 10th International Congress on Finite Fields and their Applications (Fq 10), held July 11-15, 2011, in Ghent, Belgium. Research on finite fields and their practical applications continues to flourish. This volume's topics, which include finite geometry, finite semifields, bent functions, polynomial theory, designs, and function fields, show the variety of research in this area and prove the tremendous importance of finite field theory.
