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: 754
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.

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

Author: Kenneth J. M. MacLean
Publisher: Loving Healing Press
ISBN: 1932690999
Category: Mathematics
Page: 153
View: 6990
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)

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: 4074
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.

Amazing Math

Introduction to Platonic Solids
Author: Sunil Tanna
Publisher: CreateSpace
ISBN: 9781503084858
Page: 82
View: 5251
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.

3D Origami Platonic Solids and More

Author: John Montroll
Publisher: Createspace Independent Pub
ISBN: 9781480217515
Category: Crafts & Hobbies
Page: 120
View: 5427
Polyhedra are incredibly beautiful shapes. You can now fold, display, and exhibit these models. This collection teaches you how to fold around 30 models, created and diagrammed by origami master John Montroll. Step-by-step instructions show how to make detailed models including the Tetrahedron, Sunken Tetrahedron, Cube, Dodecahedron, Hexagonal Trapezohedron, and more. Information about these polyhedra is included. The folding techniques combine origami with geometry. The models include all five Platonic Solids, sunken versions of each, and models with color effects. By folding from origami paper (white on one side, colored on the other) many stunning colorful patterns can be achieved. There is a section on variations of Archimedean Solids. There are two sections on Octahedra and Dodecahedra, polyhedra with eight and twelve sides. This adds variety to families of shapes including a prism, antiprism, dipyramid, and trapezohedron. The folding methods for each of these imaginative models are quite different. All are original designs, using the latest in folding techniques. Each model is folded from a single square, which makes them more amazing and satisfying. They range from simple to complex. These unique designs are masterworks.

Making Geometry

Exploring Three-dimensional Forms
Author: Jon Allen
Publisher: N.A
ISBN: 9780863159145
Category: Art
Page: 136
View: 3831
Professional guide to making three-dimensional models of all the Platonic and Archimedian solids in step-by-step instructions.

Drawing Geometric

Tools and Inspirations to Create Amazing Geometric Drawings
Author: Tilman Zitzmann
Publisher: Rock Point Gift & Stationery
ISBN: 1631061658
Category: Art
Page: 300
View: 2314
Let your creativity flow by drawing amazing geometric shapes! Whether you're a beginning artist looking for a way to get in touch with your creative side, a harried executive looking for a meditative hobby to reduce stress, or are already an experienced artist, learning to draw geometrically can expand your horizons, giving you a new angle on how you view your world. Even if the thought of drawing daunts you, anyone can draw simple shapes like triangles, circles, squares, and hexagons. This kit will show you how to put those shapes together in surprising ways and patterns. This kit includes: - Hypotroid Spirograph Stencil Ruler for creating amazing spiral drawings - Two 8x6 geometric drawing stencils featuring a wide variety of geometric shapes - 112 page drawing tablet with illustraitions and prompts to guide you on your journey of drawing geometric - Plus empty pages for your own amazing creations!


The Geometric Bridge Between Art and Science
Author: Jay Kappraff
Publisher: World Scientific
ISBN: 9789812811394
Category: Science
Page: 486
View: 4617
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."

Introduction to Tessellations

Author: Dale Seymour,Jill Britton
Publisher: Dale Seymour Publication
ISBN: 9780866514613
Category: Mathematics
Page: 256
View: 3122
Presents an introduction to tessellations and geometric design, including polygons, Islamic art designs, Escher-type tessellations, and tessellating letters, along with step-by-step instructions for creating tessellations.

Platonic & Archimedean Solids

Author: Daud Sutton
Publisher: Bloomsbury Publishing USA
ISBN: 0802713866
Category: Mathematics
Page: 58
View: 7646
Looks at the relationship between the five Platonic and thirteen Archimedean solids.

Curve Stitching

The Art of Sewing Beautiful Mathematical Patterns
Author: Jon Millington
Publisher: Parkwest Publications
ISBN: 9780906212653
Category: Crafts & Hobbies
Page: 96
View: 4847
Curve Stitching is a creative, practical activity with a strong mathematical background. This book explains the technique and there is a good selection of beautiful designs, together with "stitch-by-stitch" sewing plans.

Creative Constructions

Designs and Drawings
Author: Dale Seymour,Reuben Schadler
Publisher: N.A
ISBN: 9781564510808
Category: Generation of geometric forms
Page: 62
View: 9135

Ruler and Compass

Practical Geometric Constructions
Author: Andrew Sutton
Publisher: Bloomsbury Publishing USA
ISBN: 0802717764
Category: Mathematics
Page: 64
View: 7184
An introduction to geometry without measurements.

The Geometry Code

Universal Symbolic Mirrors of Natural Laws Within Us; Friendly Reminders of Inclusion to Forgive the Dreamer of Separation
Author: Bruce Rawles
Publisher: Elysian Publishing
ISBN: 9780965640572
Category: Geometry
Page: 218
View: 9351
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.

Modeling of Curves and Surfaces with MATLAB®

Author: Vladimir Rovenski
Publisher: Springer Science & Business Media
ISBN: 0387712771
Category: Mathematics
Page: 452
View: 6578
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.

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: 2035
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.

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: 3193
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.

Polyhedron Models

Author: Magnus J. Wenninger
Publisher: Cambridge University Press
ISBN: 9780521098595
Category: Mathematics
Page: 208
View: 3938
An explicit guide to the geometric principles, design, and construction of complex polyhedral figures

Dual Models

Author: Magnus J. Wenninger
Publisher: Cambridge University Press
ISBN: 9780521543255
Category: Mathematics
Page: 172
View: 9842
An enthusiastic presentation of the complex set of uniform duals of uniform polyhedral shapes.

The Mathematics Lover's Companion

Masterpieces for Everyone
Author: Edward R. Scheinerman
Publisher: Yale University Press
ISBN: 0300223005
Category: Mathematics
Page: 296
View: 6220
Twenty-three mathematical masterpieces for exploration and enlightenment