Geometry Papers

Contributor to the eGranary Library at the University of Iowa

I am providing newly typeset pages from the Second Edition of the book, replacing the old rubbishing HTML 4 pages. The digital version of the Second Edition is available now; the print version is coming in early 2019.

Note: These papers do not contain the reference charts, bookmarks, and links to each section and Figure, as does the book. But they are a lot easier to read than the old ones!

The Platonic Solids

• The Tetrahedron

• The Cube

• The Octahedron

• The Icosahedron

• The Dodecahedron

Semi-Regular Polyhedra

• The Star Tetrahedron

• The Rhombic Dodecahedron

• The Cube Octahedron (Vector Equilibrium)

• The Icosa-Dodecahedron

• The Rhombic Triacontahedron

• The Nested Platonic solids

• The Truncated Icosahedron (Soccer Ball) [Book Only]

Phi and the Pentagon

• Introduction to the Phi ratio

• The Fibonacci Series

• Properties of Phi and "Phi math"

• The Construction of the Pentagon Part I

• The Construction of the Pentagon, Part II

• The Composition of the Pentagon

• The Decagon

Phi and the Geometry of Life. A paper I uploaded to Academia.edu

• Phi and the Geometry of Life

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unconverted HTML

Spirals

• Constructing a Golden Mean Spiral

• A Geometric Determination of the Equation of the Golden Mean Spiral

Having fun with Geometry!

• 2 Dimensional Geometry

• 3 Dimensional Geometry

• The Geometry of Harmony

An interesting method of determining square roots:

The Geometric Determination of Square Roots

The Binary Circle/Sphere Pattern and the Binary Spiral:

Properties of The Binary Circle/Sphere Pattern

"I'm studying to become a carpenter and earlier this year I got a challenge to make an icosahedron from 10cm by 10cm by 10cm cube. Well, it didn't work out at all since I was totally clueless about the angles etc. I just couldn't figure them out by myself.

"After reading your articles I think I understand platonic solids a little better now. Very interesting stuff!

"Here's a few photos I'd like to share with you since you helped me so much. Without you I couldn't have constructed this."

---Otso Silvo

In these page you will find:

Geometry Book Second Edition. Rewritten for greater clarity! Including the Truncated Icosahedron.

Meticulous geometric and mathematical analyses of the 5 Platonic Solids.

Meticulous analyses of other important polyhedra. The Rhombic Triacontahedron, for example, is nature's way of nesting the 5 Platonic Solids in a beautiful and elegant fashion.

An introduction to the PhiRatio, or Golden Mean, the Fibonacci series, and "Phi Math."

A thorough scrutiny of the pentagon and the decagon. The pentagon is vitally important in the construction of the icosahedron, the dodecahedron, and other important polyhedra. Knowledge of the above three subjects is essential for those interested in sacred geometry. Otherwise, you are just farting around with stuff that you can't really understand!

Some geometric speculation. Note: These pages (under the heading unconverted HTML) have not been updated, as have the others above.

Get these papers in one convenient eBook (Click on cover) Download immediately! Over 290 illustrations, perfect for students and teachers alike. Note: Requires knowledge of algebra and elementary trigonometry.

This textbook combines clear, simple explanations and mathematical rigor. The only knowledge required is high school algebra and elementary trigonometry. In the book, I avoid trigonometry unless calculating central and surface angles. If you can understand the Pythagorean Theorem, you can understand almost everything in the book.

Special thanks to Rick Parris for his excellent free software WinGeom, which was used to create the drawings in these pages.

The Truncated Icosahedron is only available in the book.