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GeometryCode bulletin – July 2015

Friday, 31 July 2015 by Bruce Rawles

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

Vibration Station Dimension Conversation

Orthogonal Cartesian CoordinatesDave Cohen (a.k.a. Davie Crockett) and I shared this conversation about our dualistic dimensions and dizzying dimensionality on 19 July 2015, on his LA Talk Radio show. We started our talk by looking at space and time … and ended up exploring our universally shared origin of Oneness. :-)

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

  • Martin Gray’s “Places of Peace and Power” website is always a visual treat for virtual visits to vibrant parts of the planet; his commentary adds to the appreciation of egalitarian inclusiveness, encouraging compassion, tolerance and kindness, since we’re all in the same Culture! :-) … and shifting the scale from terrestrial to both extremes of space:
  • Reality doesn’t exist until we measure it, quantum experiment confirms – Doesn’t it seem that most of the time, we still act as though modern physics never happened? :-) “… reality does not exist if you are not looking at it.”
  • Six Things Everyone Should Know About Quantum Physics (another quick slideshow reminder that, as Werner Heisenberg said, “Not only is the universe stranger than we think, it is stranger than we can think.”
  • Some physicists believe we’re living in a giant hologram — and it’s not that far-fetched … we probably won’t see ‘unconscious guilt’ as the underlying purpose for the universe in physics books any time soon, but it’s still interesting to follow how modern physics keeps leading inexorably back to the mind. :-)
  • Fellow geometer, Ed Kellogg alerted us to these interesting-looking books: A Mathematical Space Odyssey: Solid Geometry in the 21st Century and Thinking Geometrically: A Survey of Geometries
  • … as well as this page about DNA Origami
  • ESPL: Dances of the Planets – We’ve featured John Martineau’s solar system geometries before, but it’s been a while; here are some elegant illustrations of a few of his discoveries; thanks to Nancy B. for sending this our way.
  • A short video about the vector equilibrium from Nassim Haramein’s organization: “The Tree of Life expresses the geometry of the fabric of the vacuum of space.”
  • This video: Hexagonal Grids in Art History by Ryan Murtha explores the idea of hexagonal recursive underpinnings behind numerous art classics. Update (30Dec2015): Check out Ryan’s new website GeometryAndTheology.com
  • I suspect many more of us than just John Horton Conway (inventor of the mathematical “Life” game) and myself have had polyhedral ‘stalactites’ adorning our abodes over the years.

Projected Hologram Universe graphic

(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.

Filed Under: 2015 Bulletins, 3D Geometries, Bulletins, sacred geometry interviews, sacred geometry news

GeometryCode bulletin for April 2015

Thursday, 30 April 2015 by Bruce Rawles

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

Metatron’s Cube art by Jarrod Bray

Occasionally I get interesting, unsolicited submissions such as this one by artist Jarrod Bray, who finds artistic inspiration from Metatron’s Cube as a starting point. Here’s one of the images (slightly retouched to bring out the contrast) he sent me recently.

Jarrod Bray - Metatron's Cube inspired Art

Fibonacci proportions in original Apple Computer logo

Like so many ubiquitous iconic images we take for granted, here’s a now-classic example of an everyday symbol (which happens to represent the company whose computing equipment I’m using to craft this bulletin) showing Fibonacci number underpinnings – note the 1, 2, 3, 5, 8 and 13 proportions, Fibonacci spiral and simple geometric archetypes – used in the image construction. Thanks to Nancy for sending this timely (pun intended) image.

Apple Computer Logo showing Fibonacci number proportions

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

  • Check out these fun and interesting animated math gifs, including fractal cycloids, rotating hypercubes, seed/flower-of-life morphings, and more
  • Levitating superconductor discs, anyone? An interesting TED talk about quantum locking and levitation.
  • Nassim Haramein’s graphic showing earth-moon proportions and some interesting ‘273 coincidences’ as well as related proportions of the Great Pyramid

(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.

Filed Under: 2015 Bulletins, 2D Geometries, 3D Geometries, Bulletins, Numbers and Proportions, sacred geometry art, sacred geometry news

GeometryCode bulletin for March 2015

Tuesday, 31 March 2015 by Bruce Rawles

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

Buckyball turns 30

Buckyball discovered in 1985In 1985, a new form of carbon molecule was discovered with 60 carbon atoms (C60) which was named the “Buckyball” in honor of Buckminster Fuller’s nickname “Bucky” and the general class of materials were christened as “Fullerenes.” If you’ve ever examined the geometry of a geodesic dome, the familiar pattern of triangle-subdivided hexagons and pentagons will intuitively remind you that this shape is a close approximation of a sphere using linear elements. This quasi-rounded shape’s closeness to a sphere, combined with Fuller’s ‘tensegrity‘ – the robustness of using only triangular elements – contributes to it’s outstanding strength for a given amount of structural material; I decided to build a geodesic dome home in 1978 after seeing a Cathedralite Dome (the only vendor at the time that paid royalties to Bucky Fuller) that had a massive oak tree crash onto it… Only a few asphalt shingles needed to be replaced; any other structure would have likely been demolished by the tonnage of the oak’s limbs. Another property owing to the spherical mimicry is the close-to-maximal amount of enclosed volume for a given amount of structural material; a very efficient shape indeed!

Here’s more about these interesting geometric nano-materials that assume the familiar Archimedean Solid (polyhedron) shape of Truncated Icosahedron; most folks think of the soccer ball shape and a quote from the related Wikipedia article on them:

“The discovery of fullerenes greatly expanded the number of known carbon allotropes, which until recently were limited to graphite, diamond, and amorphous carbon such as soot and charcoal. Buckyballs and buckytubes have been the subject of intense research, both for their unique chemistry and for their technological applications, especially in materials science, electronics, and nanotechnology.”

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

  • In Fake Universes, Evidence for String Theory
  • A paper on golden spirals: Alloy Sequence – Alloy Spiral by T. R. Phillips
  • thanks to my sister for alerting me to Andrew Norman’s Sacred Geometry with plans of Chartres Cathedral and music inspired by it; his music has won a Berlin Prize
  • Deep space galactic doppler imaging: Best 3D View of Deep Universe Reveals Astonishing Details (Video)
  • A nice photo blog with imagery of the Great Pyramid and the Giza Plateau near Cairo, Egypt
  • video: Optical Glass Sculptures by fine art glass artist Jack Storms – The Glass Sculptor he uses Fibonacci proportions in his 3D glass work.
  • Classic new age music “Angels of Comfort” by Iasos
  • a Sacred Geometry Facebook page
  • Robin Eley – Artist – Troika, squaring the circle, Kohn Gallery thanks to another fellow geometer, Liberty McGeo, for the heads-up! :-)

SquaringTheCircle-Screen Shot 2015-01-31 at 12.55.52 PM

(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.

Filed Under: 2015 Bulletins, 3D Geometries, Archimedean Solids, polyhedra, sacred geometry art, sacred geometry news, sacred geometry videos

GeometryCode bulletin for February 2015

Saturday, 28 February 2015 by Bruce Rawles

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

Lots of interesting geometric images, videos and links this month

I’ll resume featured content next month; meanwhile, enjoy a plethora of fascinating things in the world of geometrical and related interests; I had another fun conversation with David Cohen, too.

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

Blooms-StrobeAnimatedSculptures-Screen Shot 2015-01-31 at 1.07.12 PM

Blooms-StrobeAnimatedSculptures-Screen Shot 2015-01-31 at 1.06.09 PM

  • Blooms: Strobe-Animated Sculptures – exquisite Fibonacci blossom videos! Note the connection to Michael Schneider’s pinecone Fibonacci examples in last month’s bulletin. Here’s the write-up featuring the golden angle: “What you are viewing in each of the above videos is a bloom spinning at 550 RPMs while being videotaped at 24 frames-per-second with a very fast shutter speed (1/4000 sec). The rotation speed is carefully synchronized to the camera’s frame rate so that one frame of video is captured every time the bloom turns ~137.5º—the golden angle. Each petal on the bloom is placed at a unique distance from the top-center of the form. If you follow what appears to be a single petal as it works its way out and down the bloom, what you are actually seeing is all the petals on the bloom in the order of their respective distances from the top-center. Read on to learn more about how these blooms were made, why the golden angle is such an important angle, and how these are related to the Fibonacci numbers.”
  • Sacred Geometry 2015 Conference in New York: Roger Green’s conference in April 2015; more details when available
  • FaceBook pages of interest:  Spirit Science, Fractal Enlightenment, Flower of Life Society/Culture Website, Phi – 1:1.618 – the Golden Ratio Community, Nassim Haramein
    Public Figure, Applied Sacred Geometrics TV, Cosmometry Facebook page
  • Constructed using over one thousand aluminium and polished copper drops, an indoor rain installation has wowed visitors to Singapore’s Changi International Airport
  • Nigel Stanford’s music videos: Cymatics, TimeScapes, and Solar Echoes music; for more about Cymatics, check out Jeff Volk’s Cymatics Source website and Adam Reed’s Cymascope imagery; more on the Cymascope.
  • We all get Academy Awards for acting! David Cohen and Bruce Rawles talk about luminary theatrics; Dave (a.k.a. Davie Crockett) and I shared a conversation on 22 February 2015, on his LA Talk Radio show. Our conversation theme coincided with the annual Academy Awards that evening, so we had fun examining the theater dream metaphors we’re all living and how – as Shakespeare said – all the world’s a stage.
  • 3Quarks » Platonic Solids has rotating polyhedra animations for the 5 regular Platonic Solids
  • “Bucky” Buckminster Fuller Future Organization is calling for artists for a juried show: Buckminster Fuller and the Sacred Geometry of Nature (March 1-April 6, 2015 at the Morris Library of the Southern Illinois University; here is a poster for the event.
  • 4DNucleomeThanks to fellow ‘hedronist’ a.k.a. geometer and lucid dream researcher, Ed Kellogg, for alerting me to this interesting article about geometric folding and looping in the genome: Genetic Geometry Takes Shape; check out the fun and interesting origami video, too. Recall that the cross-section of DNA’s double helix geometry is a decagon (or a pair of pentagons rotated 36° around their shared center), and one complete turn of each spiral is 34 Å (ångströms) long and 21 Å in diameter; familiar adjacent Fibonacci numbers whose ratio is part of the infinite sequence that converges on the Golden Ratio.Moore curve: stages 1 through 4 (rectangular 2-dimensional fractal)

(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.

Filed Under: 2015 Bulletins, 2D Geometries, 3D Geometries, Bulletins, Fractal Geometry, sacred geometry art, sacred geometry news, sacred geometry videos

GeometryCode bulletin for January 2015

Saturday, 31 January 2015 by Bruce Rawles

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

Fibonacci Garden: Mathematics in the Plant World – New DVD from Michael Schneider

For the past two months I indicated that I would do a more proper review of “Fibonacci Garden: Mathematics in the Plant World“, the latest DVD from Michael S. Schneider, author of the superb book A Beginner’s Guide to Constructing the Universe: Mathematical Archetypes of Nature, Art, and Science by Michael Schneider (which I often recommend as a companion to Sacred Geometry Design Sourcebook.) Earlier this month, I finally finished watching it’s generous content – give your self multiple hours to savor it, since it is packed with lavish visuals, photos and illustrations … I recommend it highly. If you’re a math educator, math historian, prime number theorist, botanist, geneticist, stock market analyst or sacred geometry enthusiast, you won’t regret getting a copy for your collection. Note the ‘golden angle’ (360°/2ø) = 137.507…° which also appears in the Blooms: Strobe-Animated Sculptures which I will describe in more detail in next month’s post. Here is a Fibonacci-inspired composition that Schneider refers to in the video: Béla Bartók – Music for Strings, Percussion and Celesta, I. Rather than write about his insightful narration and imagery, I’ll let a few screen snaps convey a sense of what the DVD contains. There are hundreds of fascinating slides in this video, covering numerous aspects of how Fibonacci numbers and related sacred geometry topics reach into myriad areas of our lives; here are just a small handful of screen shots – please forgive the hand-held cell-phone photo quality; there’s no distortion or blurriness in the actual video:

stock-market-FibonacciGarden-MichaelSchneider

BelaBartok-FibonacciGarden-MichaelSchneider

puzzles-FibonacciGarden-MichaelSchneider

7thTermFibonacciGarden-MichaelSchneider

self-similarBranches-FibonacciGarden-MichaelSchneider

Kepler-quote-FibonacciGarden-MichaelSchneider

ArmViolin-proportions-FibonacciGarden-MichaelSchneider

GoldenAngle-FibonacciGarden-MichaelSchneider

RomanescoCauliflower-FibonacciGarden-MichaelSchneider

palmTreeSpirals-FibonacciGarden-MichaelSchneider

equiangularSpiral-FibonacciGarden-MichaelSchneider

In addition to an extensive bibliography at the end of the DVD, here are some of the websites that Michael references:

  • Fibonacci Quarterly
  • Fibonacci Numbers and the Golden Section
  • US Patent and Trademark Office (search using the words Fibonacci, Golden Ratio and Golden Mean)
  • USDA Plant Gallery (countless examples of Fibonacci numbers)

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

  • an introduction to the EarthStar Globe by colleague Dan Shaw; among other familiar geometric curiosities, he details 62 terrestrial vertices at intersections of the 30 rhombic elements of this unique polyhedron
  • ESPL: Dances of the Planets – ‘string art’ and other planetary orbit images inspired by The book, ‘A Little Book of Coincidence‘ by John Martineau, as were my POV-Ray planetary images, available as greeting cards, posters, apparel, calendars and more.
  • Sisyphus, Golden Globes, Polytopes, and Rhythmic Cycles – an interview of Bruce Rawles by Dave Cohen

(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.

Filed Under: 2015 Bulletins, 2D Geometries, 3D Geometries, Archimedean Solids, Bulletins, Fractal Geometry, Numbers and Proportions, Platonic Solids, polyhedra, sacred geometry art, sacred geometry books, sacred geometry calendars, sacred geometry interviews, sacred geometry music, sacred geometry news, sacred geometry videos

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  • Vandorn Hinnant – 45 Years of Dreaming with Open Eyes – Exhibition Catalogue
  • Encyclopedia of Polyhedra By George W. Hart … and other geometric gems
  • Non-Euclidean Geometries
  • M. C. Escher’s Geometry and Illusory Perspectives Revisited

Visit the archive site (authored by the late William Goldstein, a.k.a. Will Gold)
The New Invisible College - A Gateway to the Mystical Tradition of the West


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