A Geometric Analysis Of The Platonic Solids And Other Semi-Regular Polyhedra

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More About This Textbook


Getting Inside the Mind of Nature: Discover the simple but powerful mathematics of the underlying geometric figures that shape our world

Can geometry be exciting?

It can for those who can appreciate the beauty of numbers and their relationships.

This book contains a meticulous geometric investigation of the 5 Platonic Solids and 5 other important polyhedra, as well as reference charts for each solid.

Poly (many) hedron (face) means "many faces." Polyhedra are 3 dimensional figures with 4 or more faces, or sides. These polyhedra are reflections of Nature herself, and a study of them provides insight into the way the world is structured. Nature is not only beautiful, but highly intelligent. As you explore the polyhedra in this book, this will become apparent over and over again.

The book contains a geometric explanation of the Phi Ratio and Fibonacci series, and a detailed analysis of the pentagon, which forms the basis for many of these solids. The pentagon is composed entirely of Phi relationships, and is integral to a proper understanding of sacred geometry.

With over 140 full-color illustrations, this book is perfect for teachers and students of geometry alike. It is a must for those who are serious about sacred geometry.

This book is dedicated to those who can appreciate the logic of numbers and the beauty of nature, for they are both aspects of the same unifying principle.

Prerequisites: knowledge of simple algebra and elementary trigonometry. No brainiac math skills required! Only the ability to appreciate nature's own logic.

Book #1 in the Geometric Explorations Series

From Loving Healing Press (www.LovingHealing.com)

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Product Details

  • ISBN-13: 9781932690996
  • Publisher: Loving Healing Press
  • Publication date: 6/22/2007
  • Pages: 164
  • Sales rank: 817,621
  • Product dimensions: 8.50 (w) x 11.00 (h) x 0.45 (d)

Customer Reviews

Average Rating 4.5
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Sort by: Showing all of 2 Customer Reviews
  • Posted April 5, 2012


    Geometry in Nature and Nature in Mathematical Intreprations; the Author, Kenneth J.M. MacLean addresses the book for teachers, researchers and the general curious science readers. A Geometric Analysis of The Platonic Solids and Other Semi-Regular Ployhedra(With an Introduction to the Phi Ratio) has 140 full color illustrations, well known "The Fibonacci Series" and many more geometrical figures in natural existence. If the sound of these words: tetrahedron, cube, phi ratio, rectangle, icosahedron, semi-regular polyhedra, rhombic triacontahedron sound familiar to you or makes you curious to learn, i say this book is for you. Let me help you to learn first terminology in this book 'poly hedron" which means "many faces". Prerequisites for the book are the knowledge of simple algebra and elementary trigonometry. No brainiac math skills required! as the author tells us.

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  • Posted March 31, 2012

    A good book for those who love the beauty of numbers

    “A Geometric Analysis of the Platonic Solids and Other Semi-Regular Polyhedra” by Kenneth J.M. MacLean is quite the mouthful of a title to read. The title will entice those who love numbers but will be off-putting to those who don’t, which is a shame because Mr. MacLean does a good job of showing the reader the beauty of numbers and the relationships between them.

    The book has over 140 full-color illustrations which help to demonstrate just what concept the author is trying to describe. He often gives a solid illustration and then breaks it down into its components. For example, chapter 12 is about the Rhombic Dodecahedron which has a picture of what it would look like as a solid object but then Mr. MacLean breaks it down into its components: 12 faces, 14 vertices, 24 sides or edges. He then goes on to explain why it is called a rhombus, how to find the volume, the surface angles, and the Dihedral angle. I admit that I did get a little lost in the formulas.

    My favorite parts where when the author talked about the Phi Ratio and the Fibonacci Series. The Phi Ratio is also known as the Golden Ratio and is about proportion and shows the person how to see the “relationship between one quantity and another quantity.” The Fibonacci Series is perhaps the most beautiful way to talk about nature and the universe and Mr. MacLean includes real photos in this section of a nautilus shell, a molded wax agave and a sunflower to demonstrate what the Fibonacci Series is. He also illustrates the Fibonacci Series on the human body relationships.

    This book is for those who love numbers for they will be drawn to the formulas and the illustrations and will be able to appreciate the beauty of it all. For those who find numbers and math as something to be afraid of or as something that is too hard to understand, they can still enjoy the illustrations but will be overwhelmed with the more technical nature of the book.

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