Search results for: platonic-solids

Beginner s Book of Modular Origami Polyhedra

Author : Rona Gurkewitz
File Size : 45.94 MB
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This manual features 17 easy-to-master projects involving the Platonic solids: the tetrahedron, hexahedron, octahedron, dodecahedron, and icosahedron. Includes detailed diagrams and photos of all the completed models.

Amazing Math

Author : Sunil Tanna
File Size : 42.99 MB
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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.

Polyoxometalates From Platonic Solids to Anti Retroviral Activity

Author : M.T. Pope
File Size : 33.65 MB
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MICHAEL T. POPE AND ACHIM MULLER Department of Chemistry, Georgetown University, Washington, DC 20057-2222, U.S.A.; Department of Chemistry, University of Bielefeld, D-4BOO Bielefeld 1, F.R.G. Polyoxometalates, from their discovery and early development in the final decades of the 19th century to their current significance in disciplines as diverse as chemistry, mathematics, and medicine, continue to display surprisingly novel structures, unexpected reactivities and applications, and to attract increasing attention worldwide. Most of the contributors to the present volume participated in the workshop held at the Center for Interdisciplinary Research at the University of Bielefeld, July 15-17, 1992. The choice of topics illustrates some of the variety of directions and fields in which polyoxometalates can play an important role. Although many of the leading polyoxometalate research groups are represented here, we regret that time constraints, financial limitations, and in some cases difficulties of communication did not allow us to include significant and imp- tant work from other groups outside Europe and North America. In the following we briefly review the current status of the field of po- oxometalates.

A Geometric Analysis of the Platonic Solids and Other Semi Regular Polyhedra

Author : Kenneth J. M. MacLean
File Size : 86.97 MB
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This book contains a meticulous geometric investigation of the five Platonic Solids and five other important polyhedra, as well as reference charts for each solid. (Mathematics)

Archimedean Platonic Solids

Author : Mark Shelby Adams
File Size : 23.77 MB
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Volumetric proofs of the Archimedean & Platonic Solids

Building Platonic Solids

Author : Sympsionics Design
File Size : 67.3 MB
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How can you build sturdy Platonic Solids that will hold together through to the last gluing? The templates in this book were designed to answer that question. You can build the solids directly from the templates, or use them as a model to build on colored paper, cardboard, or paper you have colored or painted yourself. The completed solids made from the templates are about 1.8 inches (4.5 cm) high, and you can also follow the instructions to build bigger solids. Each template is included in the book three times, allowing you to get practice or build them along with your friends. Includes 3 x 5 black-and-white templates for building Platonic Solids and instructions.

Key to the Platonic Solids

Author : Travis Crisp
File Size : 39.15 MB
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Learn how to draw all of the platonic solids from each of the face, edge, and vertex positions. Follow along with step by step instructions to guide you through this series of original compass and straightedge construction sequences, devised and developed by the author. These methods utilize logical assumptions based upon the known mathematical formulas for the polyhedra. Each sequence begins by drawing a circle that is assumed to share the same radius as the circumsphere of the polyhedron being drawn. By assuming a constant circumsphere radius, other assumptions can be made regarding the different relationships between the various polyhedra. This unique approach to an ancient technique provides the key to drawing the platonic solids like never before. Complete with a comprehensive introduction to the key concepts involved, this work is accessible to beginners while sure to provide many hours of challenging engagement for experts as well.

Platonic Solids

Author : Sacred Geometry Ghost XV
File Size : 57.60 MB
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This notebook is ideal to use as a journal, planner, to do list book, notebook, diary or travel log. Great and ideal gift for someone special. - 120 lined blank cream pages- Beautiful matte-finished cover. - Measures 6" wide x 9" high / 15.24 x 22.86 cm

3D Origami Platonic Solids More

Author : John Montroll
File Size : 89.24 MB
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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.

Matthew Schreiber

Author : Matthew Schreiber
File Size : 71.28 MB
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Drawing Geometric Solids

Author : Sympsionics Design
File Size : 35.76 MB
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In this book, you will find precise instructions with clear images on how to draw a range of geometric solids. The book includes both simple and more advanced drawings. Step-by-step instructional images are followed, in each case, by a full-colored picture of the finished solid, drawn with colored pencils. The instructions include those for drawing a tetrahedron, a tetrahedron inside a tetrahedron, a cube, a truncated cube, a cuboctahedron, a truncated octahedron, an octahedron inside a cube, a cube inside an octahedron, a stellated octahedron, a small stellated dodecahedron, a great stellated dodecahedron, a dodecahedron, an icosahedron, a dodecahedron inside an icosahedron, an icosahedron inside a dodecahedron, and the golden rectangles inside an icosahedron. There are also instructions on how to draw a golden ratio and a regular pentagon, hexagon and decagon with a ruler and compass.

Transformation Geometry

Author : George E. Martin
File Size : 87.76 MB
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Transformation Geometry: An Introduction to Symmetry offers a modern approach to Euclidean Geometry. This study of the automorphism groups of the plane and space gives the classical concrete examples that serve as a meaningful preparation for the standard undergraduate course in abstract algebra. The detailed development of the isometries of the plane is based on only the most elementary geometry and is appropriate for graduate courses for secondary teachers.

Platonic and Archimedean Solids

Author : Daud Sutton
File Size : 64.27 MB
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The Ancient Secret of the Flower of Life

Author : Drunvalo Melchizedek
File Size : 62.66 MB
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Here, Drunvalo Melchizedek presents in text and graphics the first half of the Flower of Life workshop, illuminating the mysteries of how we came to be, why the world is the way it is and the subtle energies that allow our awareness to blossom into its true beauty. Sacred Geometry is the form beneath our being and points to a divine order in our reality.We can follow that order from the invisible atom to the infinite stars, finding ourselves at each step. The information here is one path, but between the lines and drawings lie the feminine gems of intuitive understanding. You may see them sparkle around some of these provocative ideas: Explore the miracle of our existence by meandering through the wonderland of geometry, science, ancient history and new discovery, seen through the widened vision of Drunvalo and the Flower of Life.

Studies in Arabic Philosophy

Author : Nicholas Rescher
File Size : 68.78 MB
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Nicholas Rescher presents ten essays that offer the thoughts of major Arabic philosophers in history and speak to their origins in Greek philosophy, as well as the subsequent influence of Arabic philosophy on the West. Much of the material is presented for the first time in print. Topics include: the concentric structure of the universe; the concept of existence; the Theory of Temporal Modalities; the Platonic Solids; and several essays on logic.

Shapes Space and Symmetry

Author : Alan Holden
File Size : 48.17 MB
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Explains structure of nine regular solids and many semiregular solids and demonstrates how they can be used to explain mathematics. Instructions for cardboard models. Over 300 illustrations. 1971 edition.

Understanding Physics

Author : David C. Cassidy
File Size : 63.88 MB
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A thorough grounding in contemporary physics while placing the subject into its social and historical context. Based largely on the highly respected Project Physics Course developed by two of the authors, it also integrates the results of recent pedagogical research. The text thus teaches the basic phenomena in the physical world and the concepts developed to explain them; shows that science is a rational human endeavour with a long and continuing tradition, involving many different cultures and people; develops facility in critical thinking, reasoned argumentation, evaluation of evidence, mathematical modelling, and ethical values. The treatment emphasises not only what we know but also how we know it, why we believe it, and what effects this knowledge has.

3ds Max 2008 Bible

Author : Kelly L. Murdock
File Size : 68.8 MB
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A guide to the latest version of 3ds max explains how to use the software to create a variety of animation, film effects, and games.

Architecture and Geometry in the Age of the Baroque

Author : George L. Hersey
File Size : 49.60 MB
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The age of the baroque -- a time of great strides in science and mathematics -- also saw the construction of some of the world's most magnificent buildings. In this book, George L. Hersey explores the interrelations of the two developments, explaining how the advancements of geometry and the abstractions of mathematicians were made concrete in the architecture of the day. Copyright © Libri GmbH. All rights reserved.

Mathematical Snapshots

Author : Hugo Steinhaus
File Size : 50.16 MB
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Numerous photographs, diagrams explain mathematical phenomena in series of thought-provoking expositions. From simple puzzles to more advanced problems, topics include psychology of lottery players, arrangement of chromosomes in a human cell, new and larger prime numbers, more. Fascinating glimpse into the world of numbers. 1969 edition. 391 black-and-white illustrations.