Building Platonic Solids

How to Construct Sturdy Platonic Solids from Paper Or Cardboard and Draw Platonic Solid Templates with a Ruler and Compass
Author: Sympsionics Design
Publisher: N.A
ISBN: 9789526821726
Category:
Page: 44
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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 create the solids out of colored paper, cardboard, or paper you have colored or painted yourself. The completed solids made from the templates are about 1.6inches (4cm) high, and you can also follow the instructions to build larger solids. Each template is included in the book three times, allowing you to practice or build them along with your friends. Includes 3x5 black-and-white templates for building Platonic solids and instructions, and clear step-by-step images for ruler and compass constructions on how to draw the templates. * New in the second edition: * Some of the template images were moved to the same pages for easier copying for teachers. * Detailed drawing instructions for ruler and compass constructions.

Drawing Geometric Solids

How to Draw Polyhedra from Platonic Solids to Star-Shaped Stellated Dodecahedrons
Author: Sympsionics Design
Publisher: N.A
ISBN: 9789526821733
Category:
Page: 76
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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.

Drawing Circle Images

How to Draw Artistic Symmetrical Images with a Ruler and Compass
Author: Musigfi Studio
Publisher: N.A
ISBN: 9789526787862
Category:
Page: 48
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From simple to complex - use a compass to draw fascinating artistic images. This book includes step-by-step instructions for all symmetries between threefold and twelvefold. Clear and precise black-and-white illustrations will guide you. The book provides ruler and compass constructions that you can draw without using units of measurement for three-, four-, five-, six-, eight-, ten- and twelvefold symmetries. In addition, it gives dimensions in inches (and cm) for all images, which you can use on both A4 and A3 sheets.

Amazing Math

Introduction to Platonic Solids
Author: Sunil Tanna
Publisher: CreateSpace
ISBN: 9781503084858
Category:
Page: 82
View: 3857

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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.

Modeling of Curves and Surfaces with MATLAB®


Author: Vladimir Rovenski
Publisher: Springer Science & Business Media
ISBN: 0387712771
Category: Mathematics
Page: 452
View: 8953

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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.

Connections

The Geometric Bridge Between Art and Science
Author: Jay Kappraff
Publisher: World Scientific
ISBN: 9789812811394
Category: Science
Page: 486
View: 9155

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The first edition of Connections was chosen by the National Association of Publishers (USA) as the best book in OC Mathematics, Chemistry, and Astronomy OCo Professional and ReferenceOCO 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. Contents: Proportion in Architecture; Similarity; The Golden Mean; Graphs; Tilings with Polygons; Two-Dimensional Networks and Lattices; Polyhedra: Platonic Solids; Transformation of the Platonic Solids I; Transformation of the Platonic Solids II; Polyhedra: Space Filling; Isometries and Mirrors; Symmetry of the Plane. Readership: Polytechnic students, architects, designers, mathematicians and general readers."

Harmonograph

A Visual Guide to the Mathematics of Music
Author: Anthony Ashton
Publisher: Wooden Books
ISBN: 1912706059
Category: Music
Page: 64
View: 6739

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Why did Pythagoras pause outside a Blacksmith's workshop? Can the nature of Harmony really be understood visually? Why do harmonies leave gaps or 'commas' when added together? In this charming little book Anthony Ashton uses a Victorian device called a Harmonograph to tell the story of Harmony and the intervals in the scale. With useful appendices and exquisite line drawings this is a unique and original introduction to this timeless subject. WOODEN BOOKS are small but packed with information. "Fascinating" FINANCIAL TIMES. "Beautiful" LONDON REVIEW OF BOOKS. "Rich and Artful" THE LANCET. "Genuinely mind-expanding" FORTEAN TIMES. "Excellent" NEW SCIENTIST. "Stunning" NEW YORK TIMES. Small books, big ideas.

Beautiful Geometry


Author: Eli Maor,Eugen Jost
Publisher: Princeton University Press
ISBN: 1400848334
Category: Mathematics
Page: 208
View: 9687

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If you've ever thought that mathematics and art don't mix, this stunning visual history of geometry will change your mind. As much a work of art as a book about mathematics, Beautiful Geometry presents more than sixty exquisite color plates illustrating a wide range of geometric patterns and theorems, accompanied by brief accounts of the fascinating history and people behind each. With artwork by Swiss artist Eugen Jost and text by math historian Eli Maor, this unique celebration of geometry covers numerous subjects, from straightedge-and-compass constructions to intriguing configurations involving infinity. The result is a delightful and informative illustrated tour through the 2,500-year-old history of one of the most important branches of mathematics.

The Trouble With Physics

The Rise of String Theory, the Fall of a Science, and What Comes Next
Author: Lee Smolin
Publisher: HMH
ISBN: 9780547348483
Category: Science
Page: 416
View: 1480

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“A splendid, edifying report from the front lines of theorectical physics” (San Francisco Chronicle). In this illuminating book, renowned physicist Lee Smolin argues that fundamental physics—the search for the laws of nature—is losing its way. Ambitious ideas about extra dimensions, exotic particles, multiple universes, and strings have captured the public’s imagination—and the imagination of experts. But these ideas have not been tested experimentally, and some, like string theory, seem to offer no possibility of being tested. Even still, these speculations dominate the field, attracting the best talent and much of the funding, while creating a climate in which emerging physicists are often penalized for pursuing other avenues. The situation threatens to impede the very progress of science. With clarity, passion, and authority, Smolin offers an unblinking assessment of the troubles that face modern physics, and an encouraging view of where the search for the next big idea may lead. “The best book about contemporary science written for the layman that I have ever read.” —The Times (London)

A Fuller Explanation

The Synergetic Geometry of R. Buckminster Fuller
Author: Amy C. Edmondson
Publisher: Springer Science & Business Media
ISBN: 1468474855
Category: Mathematics
Page: 302
View: 4885

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In a broad sense Design Science is the grammar of a language of images rather than of words. Modern communication techniques enable us to transmit and reconstitute images without the need of knowing a specific verbal sequential language such as the Morse code or Hungarian. International traffic signs use international image symbols which are not specific to any particular verbal language. An image language differs from a verbal one in that the latter uses a linear string of symbols, whereas the former is multidimensional. Architectural renderings commonly show projections onto three mutually perpendicular planes, or consist of cross sections at differ ent altitudes representing a stack of floor plans. Such renderings make it difficult to imagine buildings containing ramps and other features which disguise the separation between floors; consequently, they limit the creativity of the architect. Analogously, we tend to analyze natural structures as if nature had used similar stacked renderings, rather than, for instance, a system of packed spheres, with the result that we fail to perceive the system of organization determining the form of such structures.

Platonic & Archimedean Solids


Author: Daud Sutton
Publisher: Bloomsbury Publishing USA
ISBN: 0802713866
Category: Mathematics
Page: 58
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Looks at the relationship between the five Platonic and thirteen Archimedean solids.

The A to Z of Mathematics

A Basic Guide
Author: Thomas H. Sidebotham
Publisher: John Wiley & Sons
ISBN: 0471461636
Category: Mathematics
Page: 488
View: 850

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Forget the jargon. Forget the anxiety. Just remember the math. In this age of cheap calculators and powerful spreadsheets, who needs to know math? The answer is: everyone. Math is all around us. We confront it shopping in the supermarket, paying our bills, checking the sports stats, and working at our jobs. It is also one of the most fascinating-and useful-subjects. Mastering math can make a difference in your career, your studies, and your daily life. If you are among the millions of people who would love to understand math but are turned away by fear of its complexity, here is your salvation. The A to Z of Mathematics makes math simple without making it simplistic. Both easy to use and easy to read, the book covers all the topics in basic mathematics. You'll learn the definitions of such terms as "proportion"and "hexomino," and grasp the concepts behind algebra, statistics, and other processes. The book's alphabetical arrangement helps you quickly home in on any topic, and its text is rich with stimulating examples, diagrams, and other illustrations that make the discussion crystal clear to every reader. Everyone will find something of interest in this wide-ranging guide to mathematics. The perfect antidote to math anxiety, this is an invaluable resource for parents and students, home schoolers, teachers, and anyone else who wants to improve his or her math skills and discover the amazing relevance of mathematics to the world around us.

Coloring Geometric Images


Author: Sympsionics Design
Publisher: N.A
ISBN: 9789526821702
Category:
Page: 48
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This full colored book contains numerous instructions and illustrated examples of colored pencil techniques that are useful when coloring geometric images. It also includes instructions on how to draw three pictures for coloring. In addition, you will find blue outlines of captivating, three-dimensional geometric shapes for coloring. You can use these as models for drawing the same shapes on your own paper. Included are an octahedron inside a cuboctahedron, a great stellated dodecahedron from two angles, three intersecting planes, a dodecahedron inside an icosahedron, an icosahedron inside a dodecahedron, a transparent rhombic dodecahedron and a small stellated dodecahedron from two angles. Each of these shapes is presented twice, with the first one already colored to help you visualize its form.

Arabic Geometrical Pattern and Design


Author: J. Bourgoin
Publisher: Courier Corporation
ISBN: 0486155315
Category: Design
Page: 204
View: 4344

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Nearly 200 examples exhibit the wide range of Islamic art, including hexagon and octagon designs, combinations of stars and rosettes, and many variations on other geometric patterns.

Mindhacker

60 Tips, Tricks, and Games to Take Your Mind to the Next Level
Author: Ron Hale-Evans,Marty Hale-Evans
Publisher: John Wiley & Sons
ISBN: 1118166434
Category: Computers
Page: 408
View: 517

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Compelling tips and tricks to improve your mental skills Don't you wish you were just a little smarter? Ron and Marty Hale-Evans can help with a vast array of witty, practical techniques that tune your brain to peak performance. Founded in current research, Mindhacker features 60 tips, tricks, and games to develop your mental potential. This accessible compilation helps improve memory, accelerate learning, manage time, spark creativity, hone math and logic skills, communicate better, think more clearly, and keep your mind strong and flexible.

The Language of Mathematics

Making the Invisible Visible
Author: Keith Devlin
Publisher: Macmillan
ISBN: 9780805072549
Category: Mathematics
Page: 352
View: 5539

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"The great book of nature," said Galileo, "can be read only by those who know the language in which it was written. And this language is mathematics." In The Language of Mathematics, award-winning author Keith Devlin reveals the vital role mathematics plays in our eternal quest to understand who we are and the world we live in. More than just the study of numbers, mathematics provides us with the eyes to recognize and describe the hidden patterns of life—patterns that exist in the physical, biological, and social worlds without, and the realm of ideas and thoughts within. Taking the reader on a wondrous journey through the invisible universe that surrounds us—a universe made visible by mathematics—Devlin shows us what keeps a jumbo jet in the air, explains how we can see and hear a football game on TV, allows us to predict the weather, the behavior of the stock market, and the outcome of elections. Microwave ovens, telephone cables, children's toys, pacemakers, automobiles, and computers—all operate on mathematical principles. Far from a dry and esoteric subject, mathematics is a rich and living part of our culture. An exploration of an often woefully misunderstood subject, The Language of Mathematics celebrates the simplicity, the precision, the purity, and the elegance of mathematics.

Visual Function

An Introduction to Information Design
Author: Paul Mijksenaar
Publisher: 010 Publishers
ISBN: 9789064503030
Category: Graphic arts
Page: 56
View: 5566

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Architects' Data


Author: Ernst Neufert,Peter Neufert,Johannes Kister
Publisher: John Wiley & Sons
ISBN: 1405192534
Category: Architecture
Page: 593
View: 7549

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This text is an essential aid in the initial design and planning of a building project. Organised largely by building type, it covers user requirements, planning criteria, basic dimensions and considerations of function and siting.

Making

Anthropology, Archaeology, Art and Architecture
Author: Tim Ingold
Publisher: Routledge
ISBN: 1136763678
Category: Social Science
Page: 176
View: 6278

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Making creates knowledge, builds environments and transforms lives. Anthropology, archaeology, art and architecture are all ways of making, and all are dedicated to exploring the conditions and potentials of human life. In this exciting book, Tim Ingold ties the four disciplines together in a way that has never been attempted before. In a radical departure from conventional studies that treat art and architecture as compendia of objects for analysis, Ingold proposes an anthropology and archaeology not of but with art and architecture. He advocates a way of thinking through making in which sentient practitioners and active materials continually answer to, or ‘correspond’, with one another in the generation of form. Making offers a series of profound reflections on what it means to create things, on materials and form, the meaning of design, landscape perception, animate life, personal knowledge and the work of the hand. It draws on examples and experiments ranging from prehistoric stone tool-making to the building of medieval cathedrals, from round mounds to monuments, from flying kites to winding string, from drawing to writing. The book will appeal to students and practitioners alike, with interests in social and cultural anthropology, archaeology, architecture, art and design, visual studies and material culture.