Looking beyond the commonplace

As above . . . so below

Geometry Papers

Contributor to the eGranary Library at the University of Iowa
Note: These papers do not contain the reference charts, as does the book. Also, the links within the pages, to the other pages, do not work -- they are local links within the compiled book.

The Platonic Solids

Semi-Regular Polyhedra

The Division into Mean and Extreme Ratio (or, The Golden Section, or Phi), and the Pentagon

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unconverted HTML

Spirals

Having fun with Geometry!

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

icosahedron

"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 pages you will find:

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, and the Fibonacci series.
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.
Geometry Book Cover Image
Get these papers in one convenient eBook (Click on cover) Download immediately! Over 140 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.

WinGeom is available at http://math.exeter.edu/rparris/wingeom.html.