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


Page: 44

View: 6483

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


Page: 76

View: 1112

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.

Amazing Math

Introduction to Platonic Solids


Author: Sunil Tanna

Publisher: CreateSpace

ISBN: 9781503084858


Page: 82

View: 9897

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.

Beginner's Book of Modular Origami Polyhedra

The Platonic Solids


Author: Rona Gurkewitz,Bennett Arnstein

Publisher: Courier Corporation

ISBN: 0486132188

Category: Crafts & Hobbies

Page: 64

View: 5441

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.

Drawing Circle Images

How to Draw Artistic Symmetrical Images with a Ruler and Compass


Author: Musigfi Studio

Publisher: N.A

ISBN: 9789526787862


Page: 48

View: 8272

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.

Modeling of Curves and Surfaces with MATLAB®


Author: Vladimir Rovenski

Publisher: Springer Science & Business Media

ISBN: 0387712771

Category: Mathematics

Page: 452

View: 3716

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.

Geodesic Math and how to Use it


Author: Hugh Kenner

Publisher: Univ of California Press

ISBN: 9780520239319

Category: Architecture

Page: 172

View: 3774

In 1976 literary critic Hugh Kenner published this fully-illustrated practical manual for the construction of geodesic domes, which had been invented 25 years previously by R. Buckminster Fuller. Now returned to print for the first time since 1990.


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: 568

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 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: 7966

“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: 4978

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.


The Geometric Bridge Between Art and Science


Author: Jay Kappraff

Publisher: World Scientific

ISBN: 9789812811394

Category: Science

Page: 486

View: 6731

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."

The Disappearing Spoon

And Other True Tales of Madness, Love, and the History of the World from the Periodic Table of the Elements


Author: Sam Kean

Publisher: Little, Brown

ISBN: 9780316089081

Category: Science

Page: 400

View: 7984

From New York Times bestselling author Sam Kean comes incredible stories of science, history, finance, mythology, the arts, medicine, and more, as told by the Periodic Table. Why did Gandhi hate iodine (I, 53)? How did radium (Ra, 88) nearly ruin Marie Curie's reputation? And why is gallium (Ga, 31) the go-to element for laboratory pranksters?* The Periodic Table is a crowning scientific achievement, but it's also a treasure trove of adventure, betrayal, and obsession. These fascinating tales follow every element on the table as they play out their parts in human history, and in the lives of the (frequently) mad scientists who discovered them. THE DISAPPEARING SPOON masterfully fuses science with the classic lore of invention, investigation, and discovery--from the Big Bang through the end of time. *Though solid at room temperature, gallium is a moldable metal that melts at 84 degrees Fahrenheit. A classic science prank is to mold gallium spoons, serve them with tea, and watch guests recoil as their utensils disappear.

Ruler and Compass

Practical Geometric Constructions


Author: Andrew Sutton

Publisher: Bloomsbury Publishing USA

ISBN: 0802717764

Category: Mathematics

Page: 64

View: 5007

An introduction to geometry without measurements.

The Life of James Clerk Maxwell

With Selections from His Correspondence and Occasional Writings


Author: Lewis Campbell,William Garnett

Publisher: Merchant Books


Category: Biography & Autobiography

Page: 421

View: 8846

An Unabridged, Digitally Enlarged Printing Of The Revised Edition With Selections From His Correspondence And Writings To Include The Cambridge Essays.

The A to Z of Mathematics

A Basic Guide


Author: Thomas H. Sidebotham

Publisher: John Wiley & Sons

ISBN: 0471461636

Category: Mathematics

Page: 488

View: 1994

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.

Drawing Futures

Speculations in Contemporary Drawing for Art and Architecture


Author: Bob Sheil,Frédéric Migayrou,Luke Pearson,Laura Allen

Publisher: UCL Press

ISBN: 1911307266

Category: Architecture

Page: 288

View: 7663

Drawing Futures brings together international designers and artists for speculations in contemporary drawing for art and architecture.Despite numerous developments in technological manufacture and computational design that provide new grounds for designers, the act of drawing still plays a central role as a vehicle for speculation. There is a rich and long history of drawing tied to innovations in technology as well as to revolutions in our philosophical understanding of the world. In reflection of a society now underpinned by computational networks and interfaces allowing hitherto unprecedented views of the world, the changing status of the drawing and its representation as a political act demands a platform for reflection and innovation. Drawing Futures will present a compendium of projects, writings and interviews that critically reassess the act of drawing and where its future may lie.Drawing Futures focuses on the discussion of how the field of drawing may expand synchronously alongside technological and computational developments. The book coincides with an international conference of the same name, taking place at The Bartlett School of Architecture, UCL, in November 2016. Bringing together practitioners from many creative fields, the book discusses how drawing is changing in relation to new technologies for the production and dissemination of ideas.

The Architecture of Continuity

Essays and Conversations


Author: Lars Spuybroek

Publisher: V2_ publishing

ISBN: 905662637X

Category: Architecture

Page: 291

View: 5695

The state of contemporary architecture is the product of a 150-year battle between the Polytechnic and the Fine Arts that has forced us into today's stalemate, one in which architecture is caught in the gaping chasm between a materialistic high-tech and an expressionistic formalism. Nevertheless, Spuybroek's aim is to mend such a rift by rethinking technology as part of our sensory apparatus, materiality as the realm of activity and agency, and structure as the product of genesis. Building on Gottfried Semper's materialist theory of architecture, Spuybroek takes us from a philosophy of technology to a surprisingly historical argumentation that insistently revives the words of John Ruskin, William Hogarth and Wilhelm Worringer. The book includes several probing essays alongside extensive conversations in which we can see Spuybroek refine and sharpen his arguments. He makes statements such as 'No, I am not a Gothic Revivalist, but almost,' or 'We should use new instruments to address old architectural problems; not to create new problems,' and even 'We should reinvent tectonics, not do away with it.' In a period of calm with regard to architectural theorization this book makes a refreshing return to the basics, thereby realigning theory, methodology and architectural form.

Unit Polyhedoron Origami


Author: Tomoko Fuse

Publisher: Japan Publications Trading

ISBN: 9784889962055

Category: Crafts & Hobbies

Page: 99

View: 7972

Contains step-by-step, illustrated instructions for completing a variety of multidimensional origami projects.

A First Course in Mathematical Modeling


Author: Frank R. Giordano,William P. Fox,Steven B. Horton

Publisher: Cengage Learning

ISBN: 1285531760

Category: Mathematics

Page: 704

View: 5389

Offering a solid introduction to the entire modeling process, A FIRST COURSE IN MATHEMATICAL MODELING, 5th Edition delivers an excellent balance of theory and practice, and gives you relevant, hands-on experience developing and sharpening your modeling skills. Throughout, the book emphasizes key facets of modeling, including creative and empirical model construction, model analysis, and model research, and provides myriad opportunities for practice. The authors apply a proven six-step problem-solving process to enhance your problem-solving capabilities -- whatever your level. In addition, rather than simply emphasizing the calculation step, the authors first help you learn how to identify problems, construct or select models, and figure out what data needs to be collected. By involving you in the mathematical process as early as possible -- beginning with short projects -- this text facilitates your progressive development and confidence in mathematics and modeling. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

Computational Morphologies

Design Rules Between Organic Models and Responsive Architecture


Author: Michela Rossi,Giorgio Buratti

Publisher: Springer

ISBN: 331960919X

Category: Technology & Engineering

Page: 234

View: 2342

This book represents an invaluable and up-to-date international exchange of research, case studies and best practice to tackle the challenges of digital technology, computer-aided design, 3D modeling, prototyping machines and computational design. With contributions from leading experts in the field of industrial design and cultural heritage, it is split into three parts. The first part explores basic rules of design, design models and shape grammar, including the management of complex forms, and proves that innovative concepts may be derived from organic models using generative design. The second part then investigates responsive design, describing how to manage the changing morphologies of buildings through pre-programmed mechanisms of real-time response and feedback embedded in inhabitable spaces. Lastly, the third part focuses on digital heritage and its capability to increase the interaction and manipulation of object and concepts, ranging from augmented reality to modeling generative tools. The book gathers peer-reviewed papers presented at the eCAADe (Education and Research in Computer-Aided Architectural Design in Europe) Regional International Symposium, held in Milan, Italy, in 2015.