Download or read book The Geometry of Higher Dimensional Polytopes written by Zhizhin, Gennadiy Vladimirovich and published by IGI Global. This book was released on 2018-08-03 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: The majority of the chemical elements form chemical compounds with molecules of higher dimension (i.e., substantially exceeding three). This fact is very important for the analysis of molecular interactions in various areas: nanomedicine, nanotoxicology, and quantum biology. The Geometry of Higher-Dimensional Polytopes contains innovative research on the methods and applications of the structures of binary compounds. It explores the study of geometry polytopes from a higher-dimensional perspective, taking into account the features of polytopes that are models of chemical compounds. While highlighting topics including chemical compounds, symmetry transformation, and DNA structures, this book is ideally designed for researchers, academicians, and students seeking current research on dimensions present in binary compounds.
Download or read book The Classes of Higher Dimensional Polytopes in Chemical Physical and Biological Systems written by Zhizhin, Gennadiy Vladimirovich and published by IGI Global. This book was released on 2022-04-08 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of the geometry of structures that arise in a variety of specific natural systems, such as chemical, physical, biological, and geological, revealed the existence of a wide range of types of polytopes of the highest dimension that were unknown in classical geometry. At the same time, new properties of polytopes were discovered as well as the geometric patterns to which they obey. There is a need to classify these types of polytopes of the highest dimension by listing their properties and formulating the laws to which they obey. The Classes of Higher Dimensional Polytopes in Chemical, Physical, and Biological Systems explains the meaning of higher dimensions and systematically generalizes the results of geometric research in various fields of knowledge. This book is useful both for the fundamental development of geometry and for the development of branches of science related to human activities. It builds upon previous books published by the author on this topic. Covering areas such as heredity, geometry, and dimensions, this reference work is ideal for researchers, scholars, academicians, practitioners, industry professionals, instructors, and students.
Download or read book Regular Polytopes written by H. S. M. Coxeter and published by Courier Corporation. This book was released on 2012-05-23 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: Foremost book available on polytopes, incorporating ancient Greek and most modern work. Discusses polygons, polyhedrons, and multi-dimensional polytopes. Definitions of symbols. Includes 8 tables plus many diagrams and examples. 1963 edition.
Download or read book The Fourth Dimension Toward a Geometry of Higher Reality written by Rudy Rucker and published by Courier Corporation. This book was released on 2014-08-18 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most talented contemporary authors of cutting-edge math and science books conducts a fascinating tour of a higher reality, the fourth dimension. Includes problems, puzzles, and 200 drawings. "Informative and mind-dazzling." — Martin Gardner.
Download or read book Introduction to the Geometry of N Dimensions written by D. M.Y. Sommerville and published by Courier Dover Publications. This book was released on 2020-03-18 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classic exploration of topics of perennial interest to geometers: fundamental ideas of incidence, parallelism, perpendicularity, angles between linear spaces, polytopes. Examines analytical geometry from projective and analytic points of view. 1929 edition.
Download or read book Nanotechnologies and Clusters in the Spaces of Higher Dimension Emerging Research and Opportunities written by Zhizhin, Gennadiy Vladimirovich and published by IGI Global. This book was released on 2020-10-09 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: Research on nanomaterials and their applications has become a trending area in various fields of study and practice. Its properties and abilities open a variety of scientific advancements that weren’t possible in past years. One specific area of research that is benefiting from the implementation of nanotechnology is the study of higher-dimensional compounds that include metallic atoms and other polytypes. There is vast potential in the study of how nanomaterials are currently being used for producing clusters in higher dimensions of space. Nanotechnologies and Clusters in the Spaces of Higher Dimension: Emerging Research and Opportunities provides emerging research exploring the theoretical and practical aspects of the production of intermetallic clusters in high dimensional spaces using nanotechnology. Featuring coverage on a broad range of topics such as intermetallic compounds, incident conservation law, and applied mathematics, this book is ideally designed for practitioners, scientists, engineers, researchers, educators, physicists, mathematicians, students, and academicians seeking current research on the use of nanomaterials in interdimensional science.
Download or read book Platonic Archimedean Solids written by and published by Bloomsbury Publishing USA. This book was released on 2002-04-01 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt: Looks at the relationship between the five Platonic and thirteen Archimedean solids.
Download or read book Geometric Regular Polytopes written by Peter McMullen and published by Cambridge University Press. This book was released on 2020-02-20 with total page 617 pages. Available in PDF, EPUB and Kindle. Book excerpt: Regular polytopes and their symmetry have a long history stretching back two and a half millennia, to the classical regular polygons and polyhedra. Much of modern research focuses on abstract regular polytopes, but significant recent developments have been made on the geometric side, including the exploration of new topics such as realizations and rigidity, which offer a different way of understanding the geometric and combinatorial symmetry of polytopes. This is the first comprehensive account of the modern geometric theory, and includes a wide range of applications, along with new techniques. While the author explores the subject in depth, his elementary approach to traditional areas such as finite reflexion groups makes this book suitable for beginning graduate students as well as more experienced researchers.
Download or read book Normal Partitions and Hierarchical Fillings of N Dimensional Spaces written by Zhizhin, Gennadiy Vladimirovich and published by IGI Global. This book was released on 2020-12-25 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the study of the structure of substances in recent decades, phenomena in the higher dimension was discovered that was previously unknown. These include spontaneous zooming (scaling processes), discovery of crystals with the absence of translational symmetry in three-dimensional space, detection of the fractal nature of matter, hierarchical filling of space with polytopes of higher dimension, and the highest dimension of most molecules of chemical compounds. This forces research to expand the formulation of the question of constructing n-dimensional spaces, posed by David Hilbert in 1900, and to abandon the methods of considering the construction of spaces by geometric figures that do not take into account the accumulated discoveries in the physics of the structure of substances. There is a need for research that accounts for the new paradigm of the discrete world and provides a solution to Hilbert's 18th problem of constructing spaces of higher dimension using congruent figures. Normal Partitions and Hierarchical Fillings of N-Dimensional Spaces aims to consider the construction of spaces of various dimensions from two to any finite dimension n, taking into account the indicated conditions, including zooming in on shapes, properties of geometric figures of higher dimensions, which have no analogue in three-dimensional space. This book considers the conditions of existence of polytopes of higher dimension, clusters of chemical compounds as polytopes of the highest dimension, higher dimensions in the theory of heredity, the geometric structure of the product of polytopes, the products of polytopes on clusters and molecules, parallelohedron and stereohedron of Delaunay, parallelohedron of higher dimension and partition of n-dimensional spaces, hierarchical filling of n-dimensional spaces, joint normal partitions, and hierarchical fillings of n-dimensional spaces. In addition, it pays considerable attention to biological problems. This book is a valuable reference tool for practitioners, stakeholders, researchers, academicians, and students who are interested in learning more about the latest research on normal partitions and hierarchical fillings of n-dimensional spaces.
Download or read book Attractors and Higher Dimensions in Population and Molecular Biology Emerging Research and Opportunities written by Zhizhin, Gennadiy Vladimirovich and published by IGI Global. This book was released on 2019-06-28 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: In studying biology, one of the more difficult factors to predict is how parents attributes will affect their children and how those children will affect their own children. Organizing and calculating those vast statistics can become extremely tedious without the proper mathematical and reproductive knowledge. Attractors and Higher Dimensions in Population and Molecular Biology: Emerging Research and Opportunities is a collection of innovative research on the methods and applications of population logistics. While highlighting topics including gene analysis, crossbreeding, and reproduction, this book is ideally designed for academics, researchers, biologists, and mathematicians seeking current research on modeling the reproduction process of a biological population.
Download or read book Handbook of Discrete and Computational Geometry written by Csaba D. Toth and published by CRC Press. This book was released on 2017-11-22 with total page 1928 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Discrete and Computational Geometry is intended as a reference book fully accessible to nonspecialists as well as specialists, covering all major aspects of both fields. The book offers the most important results and methods in discrete and computational geometry to those who use them in their work, both in the academic world—as researchers in mathematics and computer science—and in the professional world—as practitioners in fields as diverse as operations research, molecular biology, and robotics. Discrete geometry has contributed significantly to the growth of discrete mathematics in recent years. This has been fueled partly by the advent of powerful computers and by the recent explosion of activity in the relatively young field of computational geometry. This synthesis between discrete and computational geometry lies at the heart of this Handbook. A growing list of application fields includes combinatorial optimization, computer-aided design, computer graphics, crystallography, data analysis, error-correcting codes, geographic information systems, motion planning, operations research, pattern recognition, robotics, solid modeling, and tomography.
Download or read book The Fourth Dimension written by Rudy von Bitter Rucker and published by Houghton Mifflin Harcourt. This book was released on 1985 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: A detailed description of what the fourth dimension would be like.
Download or read book Biochemistry in the Space of the Highest Dimension written by Zhizhin, Gennadiy Vladimirovich and published by IGI Global. This book was released on 2024-04-29 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: In biochemistry, a critical oversight persists in neglecting molecules' higher dimensionality and its profound implications for living organisms. Despite groundbreaking research revealing the transformative properties imbued by higher dimensions, mainstream biochemistry remains entrenched in a two-dimensional paradigm, failing to recognize the intricate relationship between molecular structure and biological function. This oversight poses a significant obstacle in understanding and addressing complex diseases plaguing humanity, from cancer to neurological disorders. Biochemistry in the Space of the Highest Dimension is a groundbreaking book that pioneers a paradigm shift in biochemistry, systematically unraveling the mysteries of higher-dimensional biomolecules and their impact on living organisms. Through meticulously researched chapters addressing topics from the structure of nucleic acids to the emergence of life itself, this book provides a comprehensive framework for understanding and leveraging the power of higher dimensions in biochemistry. Bridging the gap between theory and application offers scholars and practitioners a transformative roadmap toward innovative therapies and a deeper understanding of life's complexities.
Download or read book Convex Polytopes written by Branko Grünbaum and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The original edition [...] inspired a whole generation of grateful workers in polytope theory. Without it, it is doubtful whether many of the subsequent advances in the subject would have been made. The many seeds it sowed have since grown into healthy trees, with vigorous branches and luxuriant foliage. It is good to see it in print once again." --Peter McMullen, University College London
Download or read book Lectures on Polytopes written by Günter M. Ziegler and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on a graduate course at the Technische Universität, Berlin, these lectures present a wealth of material on the modern theory of convex polytopes. The straightforward exposition features many illustrations, and complete proofs for most theorems. With only linear algebra as a prerequisite, it takes the reader quickly from the basics to topics of recent research. The lectures introduce basic facts about polytopes, with an emphasis on methods that yield the results, discuss important examples and elegant constructions, and show the excitement of current work in the field. They will provide interesting and enjoyable reading for researchers as well as students.
Download or read book An Adventure in Multidimensional Space written by Koji Miyazaki and published by Wiley-Interscience. This book was released on 1986 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: This lavishly illustrated volume provides a strikingly visual approach to geometric shapes and transformations in 2- ,3- , and 4-dimensional space. Invoking Plato's polygons, Kepler's polyhedra, and Fuller's polytopes, the author presents, by means of hundreds of beautiful illustrations (100 of them in full color), many complex designs which may be found in nature or which may be produced by computer graphics programs. This self-contained work reveals how polygons, polyhedra, and polytopes are effective tools or hieroglyphs with which we may investigate and describe the macro, medio, and micro worlds or the multi-dimensional world without any telescope or microscope and without requiring guidance from others. Forewards by Buckminster Fuller and H. S. W. Coxeter.
Download or read book The Visual Guide to Extra Dimensions written by Chris McMullen and published by CreateSpace. This book was released on 2008-08-17 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: Watch a tesseract unfold. See how the 3D cross section of a hypercube changes as the hypercube rotates. View 4D wheels with axles with a spherinder or cubinder structure. Imagine climbing a 4D staircase. Find 10 out of 120 dodecahedra of a hecatonicosachoron highlighted... all on this visual tour of the fourth dimension.The book is much more visual and conceptual than algebraic, yet it is detailed and technical, with the intention of satisfying the needs of mathematically-minded readers familiar with the fundamentals of algebra, geometry, and graphing.
