Platonic & Archimedean Solids
| Author | : |
| Publisher | : Bloomsbury Publishing USA |
| Total Pages | : 68 |
| Release | : 2002-04-01 |
| Genre | : Mathematics |
| ISBN | : 0802713866 |
Looks at the relationship between the five Platonic and thirteen Archimedean solids.
Platonic Archimedean Solids
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The Geometry Code
| Author | : Bruce Rawles |
| Publisher | : Elysian Publishing |
| Total Pages | : 218 |
| Release | : 2012-04 |
| Genre | : Geometry |
| ISBN | : 9780965640572 |
Integrate practical insights from modern physics, ancient Hermetic Laws, non-dual meta-physics, transpersonal psychology, and humor, as tools for undoing conflicting beliefs we've dreamed ourselves into. The seven Hermetic laws are explored in depth and demonstrate how a mindfulness that embraces 'other' as 'self' can reverse the typical misapplication of these inescapable laws of Mentalism, Correspondence, Vibration, Polarity, Rhythm, Cause & Effect and Generation. Ubiquitous geometric symbols, paired to each of these laws - the circle, vesica piscis, sine wave, line, spiral, fractal and yin-yang - and their countless commonplace variations, seen from the vantage point of shared interests, reflect these ideas. The inspired use of natural law restores attributes of life, love, strength, purity, beauty, perfection and gratitude to our awareness.
3D Origami Platonic Solids & More
| Author | : John Montroll |
| Publisher | : |
| Total Pages | : 120 |
| Release | : 2018-07-20 |
| Genre | : Crafts & Hobbies |
| ISBN | : 9781877656354 |
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.
Amazing Math
| Author | : Sunil Tanna |
| Publisher | : CreateSpace |
| Total Pages | : 82 |
| Release | : 2014-10-26 |
| Genre | : |
| ISBN | : 9781503084858 |
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.
Platonic and Archimedean Solids
| Author | : Daud Sutton |
| Publisher | : |
| Total Pages | : 58 |
| Release | : 2001-08 |
| Genre | : |
| ISBN | : 9781902418346 |
Whereas "Sacred Geometry" introduced readers to two-dimensional forms, "Platonic & Archimedean Solids" presents the world of three dimensions, which was understood as early as neolithic time. Daud Sutton elegantly explores the eighteen forms--from the cube to the octahedron and icosidodecahedron--that are the universal building blocks of three-dimensional space, and shows the fascinating relationships between them. For anyone interested in design, architecture, and mathematics, this will be a delight.
Polyhedron Models
| Author | : Magnus J. Wenninger |
| Publisher | : Cambridge University Press |
| Total Pages | : 224 |
| Release | : 1971 |
| Genre | : Mathematics |
| ISBN | : 9780521098595 |
he author describes simply and carefully how to make models of all the known uniform polyhedra and some of the stellated forms.
Polyhedra
| Author | : Peter R. Cromwell |
| Publisher | : Cambridge University Press |
| Total Pages | : 498 |
| Release | : 1997 |
| Genre | : Mathematics |
| ISBN | : 9780521664059 |
Polyhedra have cropped up in many different guises throughout recorded history. In modern times, polyhedra and their symmetries have been cast in a new light by combinatorics an d group theory. This book comprehensively documents the many and varied ways that polyhedra have come to the fore throughout the development of mathematics. The author strikes a balance between covering the historical development of the theory surrounding polyhedra, and presenting a rigorous treatment of the mathematics involved. It is attractively illustrated with dozens of diagrams to illustrate ideas that might otherwise prove difficult to grasp. Historians of mathematics, as well as those more interested in the mathematics itself, will find this unique book fascinating.
Euler's Gem
| Author | : David S. Richeson |
| Publisher | : Princeton University Press |
| Total Pages | : 336 |
| Release | : 2019-07-23 |
| Genre | : Mathematics |
| ISBN | : 0691191999 |
How a simple equation reshaped mathematics Leonhard Euler’s polyhedron formula describes the structure of many objects—from soccer balls and gemstones to Buckminster Fuller’s buildings and giant all-carbon molecules. Yet Euler’s theorem is so simple it can be explained to a child. From ancient Greek geometry to today’s cutting-edge research, Euler’s Gem celebrates the discovery of Euler’s beloved polyhedron formula and its far-reaching impact on topology, the study of shapes. Using wonderful examples and numerous illustrations, David Richeson presents this mathematical idea’s many elegant and unexpected applications, such as showing why there is always some windless spot on earth, how to measure the acreage of a tree farm by counting trees, and how many crayons are needed to color any map. Filled with a who’s who of brilliant mathematicians who questioned, refined, and contributed to a remarkable theorem’s development, Euler’s Gem will fascinate every mathematics enthusiast. This paperback edition contains a new preface by the author.
Beginner's Book of Modular Origami Polyhedra
| Author | : Rona Gurkewitz |
| Publisher | : Courier Corporation |
| Total Pages | : 66 |
| Release | : 2012-03-07 |
| Genre | : Crafts & Hobbies |
| ISBN | : 0486132188 |
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.
The Fifty-Nine Icosahedra
| Author | : H. S. M. Coxeter |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 52 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461382165 |
The Fifty-Nine Icosahedra was originally published in 1938 as No. 6 of "University of Toronto Studies (Mathematical Series)". Of the four authors, only Coxeter and myself are still alive, and we two are the authors of the whole text of the book, in which any signs of immaturity may perhaps be regarded leniently on noting that both of us were still in our twenties when it was written. N either of the others was a professional mathematician. Flather died about 1950, and Petrie, tragically, in a road accident in 1972. Petrie's part in the book consisted in the extremely difficult drawings which consti tute the left half of each of the plates (the much simpler ones on the right being mine). A brief biographical note on Petrie will be found on p. 32 of Coxeter's Regular Polytopes (3rd. ed. , Dover, New York, 1973); and it may be added that he was still a schoolboy when he discovered the regular skew polygons that are named after him, and are the occasion for the note on him in Coxeter's book. (Coxeter also was a schoolboy when some of the results for which he will be most remembered were obtained; he and Petrie were schoolboy friends and used to work together on polyhedron and polytope theory. ) Flather's part in the book consisted in making a very beautiful set of miniature models of all the fifty-nine figures. These are still in existence, and in excellent preservation.
