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A Geometric Analysis of the Platonic Solids and Other Semi-Regular Polyhedra (Geometric Explorations Series) Paperback – June 22, 2007
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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.
I was a little worried when I first agreed to review this book because, even though I loved Geometry in school, it has been several years since I took the class. But I found "A Geometric Analysis of the Platonic Solids and Other Semi-Regular Polyhedra" to be very reader-friendly. The author's enthusiastic approach to geometry immediately drew me in. The definitions and the clearly-defined illustrations (over 140 throughout the book) also brought me up-to-speed very quickly. This book is an excellent resource for those studying geometry and I wish that something like this had been available to me when I was in school.
The author introduces a geometric explanation of Phi Ratio, the Fibonacci Series and the Pentagon. I was particularly fascinated with the Fibonacci Series and its relationship to nature. Once you really start understanding the sequence of the Fibonacci Series it becomes really obvious in many life forms from plants to shells to the human body. It repeatedly shows the incredible intelligence behind every form of life on this planet and that nothing is created randomly. The book also includes an investigation of the five Platonic Solids and other prominent polyhedra. Each theory includes very detailed reference charts and diagrams.
The author states that "A Geometric Analysis of the Platonic Solids and Other Semi-Regular Polyhedra" is for teachers, researchers and the Generally Curious. As one of the Generally Curious I found this to be an excellent book and would recommend it to anyone who is studying Geometry or has an interest in Math. The Prerequisites listed are: knowledge of simple algebra and elementary trigonometry. No brainiac math skills required! You only need the ability to appreciate nature's own logic. I applaud the author's fascinating approach to this topic.
Book received free of charge.