Geometry Code

Sacred Geometry Media Resource Blog

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GeometryCode bulletin for March 2014

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(1) News, Events, Interviews, Workshops, Classes, Exhibits, Products, Articles, Tutorials

Cube of One Way Mirrors

a Cube of One Way Mirrors

Reminiscent of Sara Frucht’s Kaliedoscapes which also explore the interplay of light reflected on the interior surfaces of polyhedra, both Platonic and Archimedean – see this recent related post about her reVERB™ Casual Music Game – this article about a cube with flexible walls made of one-way mirrors has a neat video showing what happens when the attached bellows change the geometry from flat planar surfaces. I’d like to see a ‘walk-through’ gallery of Kaleidoscapes that allow visual and acoustical interaction with all the Archimedean and Platonic solids as an interior participant.

New York City Sacred Geometry Fest

We already mentioned this event in the January 2014 bulletin, but there’s still time left (as far as I know) to attend a conference about sacred geometry – and these don’t happen that often – in New York next month. If anyone attends (I would, but have prior commitments) please feel free to send me any interesting links or reports from this fest … and say hi to our colleagues! Here’s a page of links from their site, and an example of one of the many workshops at this event: Leonardo’s Mind: The Geometry of the Renaissance.
Sacred Geometry Fest 2014 NYC

(2) Websites, Books, Videos, Imagery, Music and Quotes

Here are a few websites and links of interest to sacred geometry enthusiasts:

(3) Request for Submissions

As always, please let me know how I might support you. Please send me any interesting items about sacred geometry or related interests … since everything is inter-related!If you would like to stay connected and network with kindred souls online, check out my pages on
Facebook, YouTube, Twitter, Pinterest and LinkedIn. I always enjoy connecting with both recent and long-time friends and colleagues and discovering new friends of friends :-)Thanks for your interest & support! :-) BTW, I always appreciate enthusiastic reviews on the Amazon SGDS book page, and the newer Amazon book page for The Geometry Code. It’s a good “win-win” way to cross-promote your work as well.

If you like to color with colored pencils (or other media), make 3-D fold-up geometric art, do stained glass, quilts, geometric arts and/or crafts, or just want an extensive reference/resource of geometric archetypes, patterns and essential line art, you might enjoy a copy of my first book, Sacred Geometry Design Sourcebook: Universal Dimensional Patterns.

If your leanings are more metaphysical … and perhaps whimsical :-) … you might enjoy my second book, The Geometry Code: Universal Symbolic Mirrors of Natural Laws Within Us; Friendly Reminders of Inclusion to Forgive the Dreamer of Separation. It was originally going to have geometry and Hermetic Laws/symbolism as a primary focus, but in 2007, a reawakened interest in the spiritual masterpiece, A Course In Miracles – thanks to Gary Renard – shifted the primary emphasis to an exploration of the two thought fundamental systems we all vacillate between, and how we can gradually shift our mind’s identity to the happy one.

Bruce Rawles
PO Box 192, Castle Rock, Colorado 80104
author of The Geometry Code book; co-author of The Geometry Code screensaver
author of Sacred Geometry Design Sourcebook
Free monthly email bulletin on sacred geometry and related subjects
You might also enjoy my blog which has lots of other fun and info in addition to these bulletins.

GeometryCode bulletin for May 2013

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(1) News, Events, Interviews, Workshops, Classes, Exhibits, Products, Articles, Tutorials

I was interviewed Monday, 6May2013 on Dr. Lorraine Hurley’s show on GCN Radio; you can listen to the archive here. Lorraine is a non-practicing MD who likes to focus on the quantum, so we talked about modern physics as well as metaphysics, and, of course, sacred geometry. I always enjoy interviews like these. :-)

(2) Websites, Books, Videos, Imagery, Music and Quotes

fractal dodecahedron

Here are a few websites and links of interest to sacred geometry enthusiasts:

Daily post updates option now available

I recently added a way to quickly and easily subscribe to automated post updates to the GeometryCode.com website. Just enter your email below where it says the “Get GeometryCode.com post updates by email” on the upper right hand corner of any page, and click the “Subscribe” button. You’ll automatically get an email containing any new posts to GeometryCode.com made the previous day. Of course, if you prefer just getting one email a month, the bulletin you’re reading now (if you’re reading this in your email program) will still continue to provide that service.

Recent reviews of the book: The Geometry Code (now celebrating it’s first year in print)

Thanks to Susan Dugan, Mike Lemieux, and Marianne O’Sheeran for their recent, kind reviews of The Geometry Code: Universal Symbolic Mirrors of Natural Laws Within Us; Friendly Reminders of Inclusion to Forgive the Dreamer of Separation. Yet another fellow author, Jonathan Joshua, wrote the first review – Thanks, Jonathan! – last year. Huge thanks also to Gary Renard, Cindy-Lora Renard and Roberta Grace for adding The Geometry Code book (with a Foreward by Gary) to the “Gary recommends” book list on Gary’s website.
The Kindle version of the book became available last September. Many thanks to all who have encouraged me to complete it, and all your support … so very appreciated! :-) BTW, if you prefer a ‘treeware’ (paperback) version, you can order it here. Here are abundant details about the book.
BTW, even if you don’t have a Kindle, there are lots of other platforms you can read the Kindle version (or any Kindle book) on, including smartphones such as iPhone and iTouch, Android, Windows Phone 7, Blackberry, Windows and Macintosh computers, and tablets like iPad and Android tablet. Enjoy! :-)
Thanks to one and all for your generous and continued support of the two versions from multiple countries, and to Gary Renard for the Foreward, and countless others for inspiration! I’ve had a number of kind reviews and endorsements. If you’d like to add yours, please send my way, and/or post on the Amazon review page here. You can find a free first chapter of the book (entitled “The Question of Identity: Two Thought Systems”) here.

Recent Radio/Webcast Interviews/Podcasts/Videos

I’ve been updating the Events page with upcoming, ongoing, and past radio and internet interviews, presentations, and more.
Among the recent past interviews I’ve participated in (with free audio archives online that you can listen to) are:

… and many more workshops, presentations, exhibits and more on the Events page.
I always enjoy talking about the non-dual Metaphysics, Psychology, Symbolism, Philosophy and more contained within the book “The Geometry Code: Universal Symbolic Mirrors of Natural Laws Within Us; Friendly Reminders of Inclusion to Forgive the Dreamer of Separation” which is available here.

(3) Request for Submissions

If you would like to stay connected and network with kindred souls online, check out my pages on
Facebook,
YouTube,
Twitter
Pinterest and
LinkedIn.
I’m enjoying connecting with both recent and long-time friends and colleagues and discovering new friends of friends :-)
As always, please let me know how I might support you. Please send me any interesting items about sacred geometry or related interests … since everything is inter-related!
Thanks for your interest & support! :-)
BTW, I always appreciate enthusiastic reviews on the Amazon SGDS book page, and the newer Amazon book page for The Geometry Code. It’s a good “win-win” way to cross-promote your work as well.
Bruce Rawles
PO Box 192, Castle Rock, Colorado 80104
co-author of The Geometry Code screensaver
author of Sacred Geometry Design Sourcebook
Free monthly email bulletin on sacred geometry and related subjects
Please join me on Facebook and LinkedIn.
You might also enjoy my blogwhich has lots of other fun and info in addition to these bulletins.

Archives of monthly email bulletins before 2012

The Geometry Code book - Sample Chapter - Cover Page 1

April 2012 bulletin

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Sacred Geometry bulletin for April 2012:

1) News, Events, Interviews, Workshops, Classes, Exhibits, Products, Articles, Tutorials
2) Websites, Books, Videos, Music and Quotes
3) Request for Submissions

1) News, Events, Interviews, Workshops, Classes, Exhibits, Products, Articles, Tutorials

The Geometry Code: Universal Symbolic Mirrors of Natural Laws Within Us; Friendly Reminders of Inclusion to Forgive the Dreamer of Separation - front cover artwork

The Geometry Code book is ALMOST ready! Hooray!

You will be able to order the book from Amazon (VERY soon!)
You will be able to order the Kindle (digital download) almost as soon!

Here’s the ‘back story’: About the time that I was finishing Sacred Geometry Design Sourcebook, I was already working on another book, which is now almost ready! Rather than reinvent the wheel, I think the Preface I wrote explains how the book came about, and gives a hint as to what it is about. I’ll upload the Table of Contents soon, too. A little ‘trivia aside’:
The Kybalion, a book about the seven Hermetic Laws, and one of the primary inspirations for this book, arrived a century ago in 1912 (at least that’s date in a copy of the book we have), so it just worked out that this book celebrates The Kybalion’s centennial anniversary! You can read the (relatively short) entire Kybalion book online here or download as a pdf here. Ever since I first read it, it seemed like it needed more examples, and depth and breadth with contemporary insights, so The Geometry Code book is my response to that idea. :-)

Chrome Zometool earrings-jewelry

“Chrome Zome” jewelry still available … for Mother’s Day (or any occasion)!

Zometool Jewelry — featuring elegant chrome-plated Zome hubs — is STILL available … and ONLY here. Nancy (our resident jeweler) can make these earrings with the bottom (Swarovski 6mm) crystal in a variety of colors in addition to the pink (rose) and jet black varieties shown here, including clear, aqua, blue, light blue, midnight blue, teal, green, purple, amethyst purple, and other colors and variations. Each earring features the unique Zometool hub (12 pentagonal holes, 20 triangular holes and 30 golden rectangle holes) with a metallic chrome finish. Chains and earring hooks will vary with styles. … (read more…)

2) Websites, Books, Videos, Imagery, Music and Quotes

Playful Geometer’s Cosmic SpaceCrafts is a line of arts and crafts integrating Sacred Geometry into their 3D models.
Here are more examples of Playful Geometer’s artistry and a sample image:Great Stellated Dodecahedron - Playful Geometer

Thanks to András, who alerted me (some months ago) to this interesting video of how triangular bits can drill square holes. Scroll down this page about the Reuleaux triangle to see a neat animation (The Reuleaux triangle rotating inside a square) showing a similar technique; note that the center of the bit must be offset from the center of the triangle for this to work.

I think I might have already (in prior bulletins) talked about Magnus Wenninger’s polyhedra and polytope models, but if you haven’t already seen this cornucopia of great models, it’s worth a look-see.

Wikipedia is such a great resource for all sorts of factual information about geometry, symbolism and more. Here are some example references (thanks to Alan Michelson):
Golden rectangle,
Truncated icosidodecahedron,
Truncated cuboctahedron,
Rhombicosidodecahedron,
Rhombicuboctahedron,
and, of course, there are gazillions more, even just perusing polyhedra in our provincial little 3-dimensional realm. :-)

3) Request for Submissions

If you would like to stay connected and network with kindred souls online, check out my pages on
FaceBook,
YouTube,
Twitter
Pinterest and
LinkedIn.
I’m enjoying connecting with both recent and long-time friends and colleagues and discovering new friends of friends :-)

As always, please let me know how I can support you. Please send me any interesting items about sacred geometry or related interests … since everything is inter-related!

Thanks for your interest & support! :-)

BTW, I always appreciate enthusiastic reviews on my Amazon SGDS book page, and it’s a good “win-win” way to cross-promote your work as well.

Bruce Rawles

PO Box 192, Castle Rock, Colorado 80104

co-author of The Geometry Code screensaver

author of Sacred Geometry Design Sourcebook

Free monthly email bulletin on sacred geometry and related subjects

Please join me on FaceBook and LinkedIn!

You might also enjoy Bruce’s blog which has lots of other information not included in these bulletins.

Archives of monthly email bulletins before 2012

Details about the contents of Sacred Geometry Design Sourcebook, instructions for creating the graphics therein, etc.

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I just found this post in the archives of my personal blog here, which properly belongs on this site, so I’m reposting on GeometryCode.com. As mentioned toward the end, I am MOST grateful for all the support everyone has given me over the years since my first book (Sacred Geometry Design Sourcebook) was initially published in 1997 and the first website to support it shortly thereafter. The article gives some specific details about the images in the book, and I’ve added a couple of notes on pages 154 and 167 in response to an inquiry from a reader in Holland this morning. Here’s the post, with additions:

=== === ===

30Jan2007 09:17 AM Filed in: Geometry-Math
Today’s post is an email conversation I had with a visitor to the intent.com website that I probably could have written a decade ago, so this might be useful to those of you who already have purchased a copy of the book (and thanks to all of you who have supported me in this way over the years!) There are a few other goodies on my site map that might also be of interest.
=================================

Hi Julian:

Many thanks for your inquiry. I got so involved with the reply, that I’ve decided to post it on my blog for today, as well as in this email; I’m grateful that you asked the question, so now I can answer it for the world

On 30 Jan 2007, at 6:54 AM, Julian wrote:

Dear Bruce

I was reading your web pages about your book SACRED GEOMETRY DESIGN SOURCEBOOK and I wondered if you could tell me whether the book provides the reader with details of how to draw the 2-D patterns for themselves or whether they are just templates without such instruction.

The simplest answer is “yes and no”, depending on which of the 1300+ images you’re referring to.

————————————

The detailed answer is (here goes!) that I cover some of the philosophy and underlying
math, concepts and archetypal ideas in the beginning of the book, and provide a
generous assortment of references in the back of the book. For the remainder
(majority of the 256 pages), I give the images as much room as possible so that
not only can the patterns be photocopies easily (I went with spiral binding just
for that reason), the image quality would be as high as possible for an 8.5″ by 11″ format.

Some of the illustrations give step-by-step procedures (in graphical form,
assuming some basic familiarity with how to use a compass and straightedge), such as:

page 44 (showing how “unit cells” for the tiling patterns can be used to create an enormously
expanded variety of additional patterns by recognizing how the space-filling shapes can be
varied; this applies to the “unit cell” examples on pages 16-43,

page 45 (showing how each of the patterns on pages 16-43 can embellished with fractal or
other inscribed detail for each of the polygons for an infinite (literally!) variety of possible
variations, (which actually also applies to the majority of the remaining images in the book;
page 237 gives a 3D example of this),

pages 46-84 have either explicit (most of these pages) or simple to observe implicit “unit cells”
which show how these can be created in a great variety of ways,

page 84 (Pentagon Rotation Grid) gives the 73.2% proportion crucial to the exact construction of this pattern,

page 85 (Genesis of the Seed of Life) shows the step-by-step “compass only” construction of this important
and universal pattern,

page 86-95 (variations on Seed of Life and Flower of Life) show how once the Seed of Life is constructed,
so many other patterns can be easily derived – Flower of Life, Hexagonal Grid, 2nd Harmonic Overlay
(which is used in Mika Feinberg’s beautiful LightSOURCE screensaver animation; see my links page
at http://www.intent.com/bruce/links.html), Tree of Life, Fruit of Life, Heart and Ankh matrices, recursions,
Metatron’s Cube, etc.),

page 95: since the Dodecahedron is the most complicated shape to derive from Metatron’s cube, the top center
illustration on this page shows which vertices are used to create the “dodecahedron 2D shadow” with small
circles highlighted in the larger image,

page 96: The general instructions for creating Nested Inscribed Polygons appear on this page,

page 100-102: other examples of the crucial proportions needed to create these image either by hand or with a computer graphics program; numerous pages provide these instructions in the text without detracting from the space given to the images,

pages 104-105, 110-113, 123-124, 128, 130, 138-139, 144-145, 155, 163, 166, 171, 176-180, 182-187: all have instructions and details on how to create the images,

page 146: very detailed step-by-step instructions for inscribing a pentagon within a circle,

page 147: very detailed step-by-step instructions for inscribing a pentagon starting from one side of a given length,

page 154: Follow the steps on page 146, making a circle with an inscribed pentagon. Extend the lines of the pentagon to make a pentagram (5 pointed star). Extend lines from the center of the pentagram through the inner vertices to make a decagon with the outer pentagram vertices defining 5 of the 10 decagon vertices. Extend the lines of the decagon to generate the lines that become the next ‘ring’ of flattened (non-regular) pentagrams. Noticing the parallel lines and intersections, one can generate fractally nested flattened pentagram rings outward or inward in either direction.

page 156: very detailed step-by-step instructions for creating a golden rectangle (including “whirling squares and more),

page 156: very detailed step-by-step instructions for dividing a line by the golden ratio,

page 157: very detailed mathematical information about golden ratio progressions and powers, illustrated graphically,

page 167:  Make a pentagram (following the steps on pages 146 or 147), then use 1 ‘arm’ of the pentagram (a Golden Triangle.) Alternately, you can make a golden rectangle, or just divide a line segment by the golden ratio (both on page 156) and then use your compass to make a golden triangle with these proportions. Once you have the golden triangle, set the compass to the small side length and swing an arc from one of the bottom vertices (intersection of two different-length sides) to one of the longer sides. Draw the line (same length as the short side) to the new intersection and you have the first smaller nested fractal golden triangle. Just keep repeating this process to make smaller golden triangles, each with side lengths 1/phi times the original.

page 188: shows how the Parthenon at the Acropolis in Athens, Greece incorporates the golden ratio

page 189: an amazing amount of data on this page about the Great Pyramid at Giza, Egypt showing phi (golden ratio) and pi proportions, and the proportions of the so-called “King’s Chamber” although the so-called “sarcophagus” (granite box) within is too large to fit through the only passage leading into that chamber, which violates the generally accepted funerary rite theory,

page 190: the classic “Measure of Man” (Vitruvian Man) by Leonardo daVinci, copied around the world, showing the golden ratio proportions in the human body,

page 191: the only known CAD drawing adaptation (to my knowledge) of Leonardo’s “Ideal Church” sketch,

page 192: detailed specifics about the Shoemaker’s Knife of Archimedes, giving several variations all showing the mathematical principle,

page 194: details of the geometry of the classic 1991 Barbury Castle, England crop circle formation,

page 195 and page 52: the details of the geometry encoded in the Sri Yantra (a classic Hindu mandala) and the cross section of the Great Pyramid at Giza, Egypt (also the “squaring the circle” conundrum), both with a 1-Phi-Square Root of Phi triangle which has a 51 degree, 51 minute slope,

page 196: numerous details common to the 5 Platonic and 13 Archimedean Solids,

pages 197-214; numerous details specific to the 5 Platonic and 13 Archimedean Solids, including how the insphere/intersphere/circumsphere/side length proportions are calculated,

pages 215-224: similar details specific to the 4 Kepler-Poinsot solids, the Star Tetrahedron (a.k.a. Stella Octangula) and related polyhedra,

pages 225-229: numerous graphics showing how the Platonic Solids relate to each other in a myriad of fascinating (awe-inspiring, really!) ways,

pages 230-235: numerous relationships between 3D polyhedra with 5-sided symmetry and the “shadow” they cast on a decagon (10-sided polygon), with construction details,

page 236: step-by-step instructions on creating an accurate drawing of the Icosahedron and Dodecahedron starting from a Golden Rectangle,

pages 237-255: generous appendices for hands-on explorers of all ages and levels of experience, including tables and charts of regular polygon angles, apothem, radius and side ratios and areas, radius ratios by coordination number for Ionic Chemical Bonding (which relates to properties of materials at the molecular and planetary levels), Fibonacci Numbers, Perfect Right Triangles (when I put the book together, I wasn’t aware of the Phi-1/Phi-Square Root of 3 Right Triangle that Mike Green of British Columbia introduced me to), Prime Numbers, extensive tables with all sorts of data on the Platonic and Archimedean Solids (useful for a variety of purposes, including model construction and computer simulation and animation, a map of planet Earth showing superimposed Platonic Solid Vertex Latitudes and (example) Longitudes, a fun stereogram with 6 Small Stellated Dodecahedra (there, I gave the clue away , a short bio of myself, 3 pages of bibliography (more on my books and links pages and blog), and unique graphical index to all the illustrations in the book. Whew! I’d almost forgotten how much I packed into this labor of love over a decade ago!

Many of the 1300+ images are somewhat self-explanatory graphically (especially if you have created the basic shapes like the Seed of Life, Golden Rectangle and a few others by hand with compass and straight-edge, which I highly recommend for anyone as mentor Keith Critchlow so aptly reminded me when reviewing my original manuscript)…

… and of course, if you are finding re-creating one of the patterns challenging, I’d be happy to answer other questions via email that I can share with other enthusiasts on my blog (which I’ll do with this reply; thanks for asking!

I’m also working on a number of related projects that will complement the book with video “hands on” procedures, etc. Stay tuned!

Sacred Geometry Toys and Tools

… and more additions below… scroll down :-)

Zometool

Zometool is easily my favorite and most versatile sacred geometry toy (and tool, since I use it in workshops to demonstrate sacred geometry proportions in both 2D and 3D, relationships between the Platonic and Archimedean Solids and much more. Here’s a page showing how Zometool can build a large number of the designs in Sacred Geometry Design Sourcebook.)


ZomeTool
ZomeTool

ZomeTool

Zometool is a superb creative geometric toy/tool/visualization system from the wizardry of Marc Pelletier! I use mine for demos and explorations of all sorts.

MUCH more about Zometool here…

Fractiles


Fractiles
Fractiles

Fractiles – Versatile geometric toys made of magnetic diamond shaped tiles

I’ve enjoyed playing — I’m just a big kid — with Fractiles for many years. I don’t even need the excuse of having younger family members visiting to bring them out and design elegant patterns with these unique magnetic tiles in 3 diamond shapes. Here are a few examples of the endless patterns that can be made in a few minutes.


Fractiles


Fractiles

Here’s a list of features from the Fractiles website:

  • Award-Winning Fractiles-7 received a Parents’ Choice Award for play and educational value, quality and design.
  • Versatile: Use these wonderful little diamond-shaped tiles to easily create seven-fold snowflakes, starbursts, spirals, bouquets of flowers, swarms of fireflies, beautiful mandalas, butterflies, spaceships, 3-D illusions, much more.
  • Elegant Geometry: The versatile elegant geometry allows anyone to create endless varieties of imaginative and beautiful designs. Designs range from very simple to infinitely complex. One can spend tireless hours discovering new levels of play and design.
  • Infinite Possibilites: Puzzle with millions of solutions — limitless combinations and diverse designs.
  • Wide Appeal: Fractiles Fans range from young children to seniors, from those with no math background to advanced math researchers.
  • Easy to Manipulate: The MAGNETIC tiles stay put – yet slide easily on their specially textured board – a helpful feature for anyone with fine motor skill problems. Magnetic Fractiles-7 is a great travel toy!
  • Builds Pattern Recognition Skills: Pattern recognition skills are key to learning. Lack of pattern recognition skills is linked to learning disabilities Fractiles-7 is so much fun you may not even notice how regular play increases your pattern recognition skills.
    “Fractiles is so popular with my first graders, that we have to have a sign up for equal turns!” – teacher Marilyn Bowker
    “My 7th and 8th graders live for free time so they can play with Fractiles.” – Sandra Bullard, The Prentice School, “Where Children with Dyslexia Learn to Learn”
  • Ethical: Production Fractiles is manufactured in the USA with no child labor or exploitation.

More about Fractiles here…

Astro-logix

Astro-logix : Rhombic Triacontahedron




Astro-logix is a unique system of glow-in-the-dark hubs and day-glow cylinders to make a phenomenal variety of 2D and 3D geometric models. There’s MUCH more imagery and info on the Astro-logix website. Here’s a video of a Platonic nest made with Astro-logix components.

Spirograph
Spirograph: One of my favorite childhood geometric toys is back again. :-)
More geometric toys…