Search results for: platonic-and-archimedian-solids

Platonic and Archimedean Solids

Author : Daud Sutton
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Geomag Polyhedron

Author : Source: Wikia
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This book consists of articles from Wikia or other free sources online. Pages: 47. Chapters: Archimedean Solid, Deltahedron, Dodecahedron, Johnson Solid, Near Miss, Nested Polyhedra, Nice Try, Platonic Solid, Pseudo Polyhedron, Rhombic Panels, Ring, Archimedean Solids, Icosidodecahedron, Rhombicosidodecahedron, Truncated dodecahedron, -deltahedron, -deltahedron, -deltahedron, -deltahedron, -deltahedron, -deltahedron, -deltahedron, -deltahedron, -deltahedron, -deltahedron, -deltahedron, 128-hedron, Creased Platonic Deltahedra, Diamond, Extended Elongated Hexagonal Antiprism, General Deltahedron, Lobel Frames, Pentagonal Deltahedron, Pentagonal Torus, Snub Disphenoid, Snub Expanded-deltahedron, Snub Expanded-deltahedron, Snub Expanded Snub Disphenoid, Spiral Deltahedron, Spiral spheres, Tori, Annular Dodecahedron, Dodecahedron composed of 5 wobbly cubes, Reinforced Dodecahedron, Bilunabirotunda, Gyrobifastigium, Snub Disphenoid, 13-gon Circle, 26gon circle, Bi Elongated Rhombic Triacontahedron, Elongated Rhombic Triacontahedron, Enneagonal Polyhedron, Pseudosphere From Geomag Box, Rhombic Triacontahedron, Snub Expanded Tetrated Dodecahedron, Snub Expanded Triangular Prism, Stellated Rhombic Triacontahedron, Tetrated Dodecahedron, Truncated Icosahedron, Truncated Cuboctahedron of Cubes, Heptagonal Ring, Amafirlian Cube, Annular Dodecahedron, Dodecahedron composed of 5 wobbly cubes, Platonic solids, Reinforced Dodecahedron, -deltahedron, -deltahedron, -deltahedron, -deltahedron, -deltahedron, -deltahedron, -deltahedron, -deltahedron, -deltahedron, -deltahedron, -deltahedron, 128-hedron, 13-gon Circle, 26gon circle, 30-gon Circle of Prisms, Amafirlian Cube, Amafirlian Cuboctahedron, Amafirlian Elongated Square Gyrobicupola, Amafirlian Rhombicuboctahedron, Amafirlian Rhombic Dodecahedron, Annular Dodecahedron, Archimedean Solids, Augmented Truncated Dodecahedron, Bilunabirotunda, Bi Elongated Rhombic Triacontahedron, Creased Platonic Deltahedra, Curved Triangle Using 30-

Amazing Math

Author : Sunil Tanna
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This book is a guide to the 5 Platonic solids (regular tetrahedron, cube, regular octahedron, regular dodecahedron, and regular icosahedron). These solids are important in mathematics, in nature, and are the only 5 convex regular polyhedra that exist. Topics covered include: What the Platonic solids are The history of the discovery of Platonic solids The common features of all Platonic solids The geometrical details of each Platonic solid Examples of where each type of Platonic solid occurs in nature How we know there are only five types of Platonic solid (geometric proof) A topological proof that there are only five types of Platonic solid What are dual polyhedrons What is the dual polyhedron for each of the Platonic solids The relationships between each Platonic solid and its dual polyhedron How to calculate angles in Platonic solids using trigonometric formulae The relationship between spheres and Platonic solids How to calculate the surface area of a Platonic solid How to calculate the volume of a Platonic solid Also included is a brief introduction to some other interesting types of polyhedra - prisms, antiprisms, Kepler-Poinsot polyhedra, Archimedean solids, Catalan solids, Johnson solids, and deltahedra. Some familiarity with basic trigonometry and very basic algebra (high school level) will allow you to get the most out of this book - but in order to make this book accessible to as many people as possible, it does include a brief recap on some necessary basic concepts from trigonometry.


Author : Peter R. Cromwell
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This book comprehensively documents the many and varied ways that polyhedra have come to the fore throughout the development of mathematics.


Author : Jay Kappraff
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The first edition of Connections was chosen by the National Association of Publishers (USA) as the best book in ?Mathematics, Chemistry, and Astronomy ? Professional and Reference? in 1991. It has been a comprehensive reference in design science, bringing together in a single volume material from the areas of proportion in architecture and design, tilings and patterns, polyhedra, and symmetry. The book presents both theory and practice and has more than 750 illustrations. It is suitable for research in a variety of fields and as an aid to teaching a course in the mathematics of design. It has been influential in stimulating the burgeoning interest in the relationship between mathematics and design. In the second edition there are five new sections, supplementary, as well as a new preface describing the advances in design science since the publication of the first edition.

Polyoxometalates From Platonic Solids to Anti Retroviral Activity

Author : Michael Pope
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The early transition elements, especially vanadium, molybdenum, and tungsten, form a vast number of polyoxoanions with remarkable structures, unprecedented combinations of properties, and relevance to disciplines ranging from mathematics to medicine. Although the first examples of these substances were described in the mid-19th century, it is only within the last 20--30 years that the field has begun to receive the attention it deserves. This book contains 28 review chapters by leading investigators who participated in an international workshop held in Bielefeld in July 1992. It provides a survey of recent and current activity in this field - including new synthetic methods, and new structural types; topological analysis of polyhedral structures; discrete polyoxoanions as models for metal oxide lattices, magnetic interactions and domains; donor--acceptor and host--guest chemistry; organic and organometallic derivatives; mixed valence and electron transfer; homogeneous and heterogeneous redox and acid catalysis; photochemistry and photocatalysis; polyoxoanion-protein chemistry; antitumor and anti--HIV activity.

3D Origami Platonic Solids More

Author : John Montroll
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Polyhedra are incredibly beautiful shapes. Illustrated step-by-step diagrams show how to fold a collection of around 30 models including the five Platonic Solids, sunken versions of each, models with color patterns, variations on Archimedean Solids, and more. Each model is folded from a single uncut square. They range from simple to complex.

Chemical Modelling

Author : Alan Hinchliffe
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Chemical Modelling: Applications and Theory comprises critical literature reviews of molecular modelling, both theoretical and applied. Molecular modelling in this context refers to modelling the structure, properties and reactions of atoms, molecules & materials. Each chapter is compiled by experts in their fields and provides a selective review of recent literature. With chemical modelling covering such a wide range of subjects, this Specialist Periodical Report serves as the first port of call to any chemist, biochemist, materials scientist or molecular physicist needing to acquaint themselves of major developments in the area. Specialist Periodical Reports provide systematic and detailed review coverage in major areas of chemical research. Compiled by teams of leading authorities in the relevant subject areas, the series creates a unique service for the active research chemist, with regular, in-depth accounts of progress in particular fields of chemistry. Subject coverage within different volumes of a given title is similar and publication is on an annual or biennial basis. Current subject areas covered are Amino Acids, Peptides and Proteins, Carbohydrate Chemistry, Catalysis, Chemical Modelling. Applications and Theory, Electron Paramagnetic Resonance, Nuclear Magnetic Resonance, Organometallic Chemistry. Organophosphorus Chemistry, Photochemistry and Spectroscopic Properties of Inorganic and Organometallic Compounds. From time to time, the series has altered according to the fluctuating degrees of activity in the various fields, but these volumes remain a superb reference point for researchers.

Classic Polyhedra Origami

Author : John Montroll
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Presents step-by-step instructions showing paperfolders how to create thirty-three variations on the geometric forms known as polyhedra.

Modeling of Curves and Surfaces with MATLAB

Author : Vladimir Rovenski
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This text on geometry is devoted to various central geometrical topics including: graphs of functions, transformations, (non-)Euclidean geometries, curves and surfaces as well as their applications in a variety of disciplines. This book presents elementary methods for analytical modeling and demonstrates the potential for symbolic computational tools to support the development of analytical solutions. The author systematically examines several powerful tools of MATLAB® including 2D and 3D animation of geometric images with shadows and colors and transformations using matrices. With over 150 stimulating exercises and problems, this text integrates traditional differential and non-Euclidean geometries with more current computer systems in a practical and user-friendly format. This text is an excellent classroom resource or self-study reference for undergraduate students in a variety of disciplines.

Architecture and Geometry in the Age of the Baroque

Author : George L. Hersey
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The age of the Baroque—a time when great strides were made in science and mathematics—witnessed the construction of some of the world's most magnificent buildings. What did the work of great architects such as Bernini, Blondel, Guarini, and Wren have to do with Descartes, Galileo, Kepler, Desargues, and Newton? Here, George Hersey explores the ways in which Baroque architecture, with its dramatic shapes and playful experimentation with classical forms, reflects the scientific thinking of the time. He introduces us to a concept of geometry that encompassed much more than the science we know today, one that included geometrics (number and shape games), as well as the art of geomancy, or magic and prophecy using shapes and numbers. Hersey first concentrates on specific problems in geometry and architectural design. He then explores the affinities between musical chords and several types of architectural form. He turns to advances in optics, such as artificial lenses and magic lanterns, to show how architects incorporated light, a heavenly emanation, into their impressive domes. With ample illustrations and lucid, witty language, Hersey shows how abstract ideas were transformed into visual, tactile form—the epicycles of the cosmos, the sexual mystique surrounding the cube, and the imperfections of heavenly bodies. Some two centuries later, he finds that the geometric principles of the Baroque resonate, often unexpectedly, in the work of architects such as Frank Lloyd Wright and Le Corbusier. A discussion of these surprising links to the past rounds out this brilliant reexamination of some of the long-forgotten beliefs and practices that helped produce some of Europe's greatest masterpieces.

Lehrbuch der Topologie

Author : Herbert Seifert
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The Geomantic Year

Author : Richard Leviton
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The spiritual world blesses the Earth at least 58 times a year-here's how you can join the party. Do you think folklore customs about solstices and equinoxes and other regular celebration days are quaint holdovers from the past? Not so. Do you sometimes wish there were a way to include the entire planet in a meditation practice? There is, and it's called the geomantic year. At least 58 times a year the spiritual world-angels, archangels, Ascended Masters, Star-Angels, even the Supreme Being-tunes in to the Earth, blesses, and even heals it in real-time day-long events. Our planet is constantly receiving input from the cosmos and heavenly realms. It's all part of a rhythmic maintenance calendar in which the Earth is enlivened, and all of humanity is invited to participate. This book shows you how. What kinds of events? On Epiphany, January 6, the Christ focuses on the planet to birth his Light. On Bifrost Paints the Planet, April 10, the Great Bear constellation envelopes the Earth in 14 rays of light. On Michaelmas, September 29, the Archangel Michael cleanses the Earth's sacred sites and all their "plumbing." Other events in the geomantic year involve stars, Nature Spirits, holy mountains, River-gods, Pleiadians, Hollow Earth dwellers, Grail Kings, volcano spirits, the Great Mother, and much more. The Geomantic Year documents 58 festival dates that focus on the Earth through its sacred sites, and it provides 58 simple meditations to help you participate. And it offers 12 informative essays linking Earth energies with hot topics such as the Illuminati and world control, parallel universes, the world's gold supply, the Ghost Dance, the Fall of Man, Earth and climate changes, and the apocalyptic year 2012. Why not get out your appointment book and pencil in a few dates: the Earth's expecting you!

Telecommunication Networks

Author : Eugenio Iannone
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Many argue that telecommunications network infrastructure is the most impressive and important technology ever developed. Analyzing the telecom market’s constantly evolving trends, research directions, infrastructure, and vital needs, Telecommunication Networks responds with revolutionized engineering strategies to optimize network construction. Omnipresent in society, telecom networks integrate a wide range of technologies. These include quantum field theory for the study of optical amplifiers, software architectures for network control, abstract algebra required to design error correction codes, and network, thermal, and mechanical modeling for equipment platform design. Illustrating how and why network developers make technical decisions, this book takes a practical engineering approach to systematically assess the network as a whole—from transmission to switching. Emphasizing a uniform bibliography and description of standards, it explores existing technical developments and the potential for projected alternative architectural paths, based on current market indicators. The author characterizes new device and equipment advances not just as quality improvements, but as specific responses to particular technical market necessities. Analyzing design problems to identify potential links and commonalities between different parts of the system, the book addresses interdependence of these elements and their individual influence on network evolution. It also considers power consumption and real estate, which sometimes outweigh engineering performance data in determining a product’s success. To clarify the potential and limitations of each presented technology and system analysis, the book includes quantitative data inspired by real products and prototypes. Whenever possible, it applies mathematical modeling to present measured data, enabling the reader to apply demonstrated concepts in real-world situations. Covering everything from high-level architectural elements to more basic component physics, its focus is to solve a problem from different perspectives, and bridge descriptions of well-consolidated solutions with newer research trends.


Author : F. Arthur Sherk
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H.S.M. Coxeter is one of the world's best-known mathematicians who wrote several papers and books on geometry, algebra and topology, and finite mathematics. This book is being published in conjunction with the 50th anniversary of the Canadian Mathematical Society and it is a collection of 26 papers written by Dr. Coxeter.

Advances in Supramolecular Chemistry

Author : G.W. Gokel
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In this volume, inorganic, organic, and bioorganic chemistry are represented in contributions from around the world. Pioneering work in self-assembled structures organized by the use of transition metals is described in chapter 1, followed by details of extensive studies of self-assembled structures formed from various biomolecules in chapter 2. The next two chapters describe the formation of spherical molecular containers and their understanding of such structures based on Platonic and Archimedean solids, and the fascinating family of synthetic peptide receptors and the interactions that can be explored using these host molecules. In chapter 5 a mixture of computational chemistry, drug design, and synthetic organic and inorganic chemistry in the development of superoxide dismutase mimics is described. The final two chapters discuss the bioorganic and supramolecular principles required for the design of synthetic artificial enzymes, and the supramolecular self-assembly and its possible role in the origin of life. It is hoped that this broad, international view of supramolecular chemistry and the many directions it leads will be of interest to those already in the field. It is also hoped that those outside the field may see extensions of their own work that will bring them into it.

Designing and Building Tessellated Polyhedra

Author : Robert Fathauer
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Polyhedra allow geometric shapes in the plane to become solids in our three-dimensional world. Tessellations in which individual tiles are lifelike motifs are a fun combination of art and mathematics. Designing and Building Tessellated Polyhedra brings these two fascinating topics together a for hands-on learning experience rich in math content. Nets for 24 different polyhedra, including all of the Platonic and Archimedean solids, are presented both with and without tessellations applied to them. This allows polyhedra to be built with ready-made designs that can be colored if desired, or printed in beautiful color using the included CD. Another option is building undecorated polyhedra that have the names and key properties printed on them. Yet another possibility is to use templates to design new tessellations that can be applied to the polyhedra. The book also contains background on polyhedra and templates for tessellated cones, cylinders, and Msbius strips. For classroom use, ten activities with worksheets, designed to address ten different specific Common Core State Standards for Mathematics are included as well. Ages 12-17

Multimodular Origami Polyhedra

Author : Rona Gurkewitz
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Explore the link between paperfolding and mathematics with this unique, well-illustrated guide to creating a world of multifaceted wonders that draws on elements of crystallography. Detailed instructions, clear diagrams.

Acta Geologica

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Fifth IEEE International Conference on Information Visualisation

Author : Ebad Banissi
File Size : 82.62 MB
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Annotation The main subjects of the July 2001 conference are computer aided geometric design, medical visualization, visualization in built environment, digital art, rendering, and visual methods for parallel and distributed programming. Topics of the 110 papers include a prototype design tool for building integrated photovoltaics, finding and characterizing candidate binding sites, visualizing capacity and load in production planning, error analysis for the evaluation of rational Bezier curves, drawing conics on a hexagonal grid, visual interaction with XML metadata, virtual access to landscapes and historic gardens at linked locations, and adaptive fairing of surface meshes by geometric diffusion. No subject index. c. Book News Inc.