Every moment is an opportunity to see the intrinsic sameness of everyone and everything – we’re all kindred spirits. – We explore, as Danushia says, seeing beyond the veil … and having fun with it! In this video conversation, Danushia Kaczmarek inteviews Bruce Rawles about “The Spirit of Science ~ Sacred Geometry ~ The Pyramids of Egypt” in her interview series about going from head to heart. We cover a wide range of subjects including Fibonacci numbers, spirals, the golden ratio, Platonic Solids, sterograms, biofeedback, catelysts, ACIM, the double helix of DNA, modern physics ideas such as quantum entanglement, the wave/particle (double slit) phenomenon, expectations in the mind and the undoing of the Newtonian world view, flat approximations for living on a spheroid, and much more. (Quick correction; in the conversation I mentioned Mauna Kea, but it’s actually Mauna Loa, Hawai’i that is at the 19.5° north latitude.)
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Sacred Geometry Design Sourcebook (SDGS) turns 20!
I printed and published the first copies of Sacred Geometry Design Sourcebook (SDGS) in December 1997. It took a year of intensive graphics work using Claris CAD – does anyone remember that Apple application? – to convert and extend numerous hand-drawn geometric illustrations into digital form. My wife (Nancy Bolton-Rawles) took an evening class and I started with an evening a week – while she was in class – learning how to use this early CAD program for something other than video routing switcher control panels and making these geometric archetypes with far more accuracy and resolution than I could possibly achieve by straightedge and compass (the classic geometer’s tools) or any other physical mechanical means. Those evenings quickly overflowed into seemingly every conceivable spare moment. I realized that these CAD drawings (plus a few other unique images such as a stereogram, some unusual tables, charts, spreadsheets and even a cameo illustration of a sphere by Nancy (who was taking art classes during that time) merited a book. There are over 1300 geometric CAD illustrations counting all the variations I placed in the margins of many of the larger full page (8.5″ x 11″) images.
It’s amazing to reflect on the journey of explorations that have branched off (fractals, anyone?) from this first book by countless colleagues. I am profoundly grateful to one and all for the links, shared discoveries, and inestimable support in 2 dimensions, 3 dimensions, 4 dimensions and beyond over the past two decades … and before and after that, too – since we’re all interconnected beyond time and space! It’s been wonderful fun to get emails, postal mails of unexpected geometrically-inspired gifts, and other correspondence via Facebook (GeometryCode.com and Geometry Code) plus other social media, etc. Thanks, everyone, for your generous and steady contributions and support over the past two decades! 🙂
If you are new to this website (or would like to peruse some of these topics again), you might want to start with this introduction to sacred geometry and then explore many years of bulletins, posts, and articles about related geometric coloring books – of which SGDS is a prime example! – and other sacred geometry art, books, calendars, food, audios and interviews, jewelry, music, news, physics, spaces, toys and videos, the golden ratio, Fibonacci numbers, other interesting numbers and proportions, the Platonic Solids and Archimedean Solids, other polyhedra, plus even some interconnections with the ancient, timeless Hermetic Laws and their relationship to modern physics … and metaphysics … which led to my second book, The Geometry Code: Universal Symbolic Mirrors of Natural Laws Within Us; Friendly Reminders of Inclusion to Forgive the Dreamer of Separation.
To commemorate this 20th anniversary month (December 2017) of SGDS, here is an illustration that I added later, but didn’t make it into the book: a fold-up pattern for the Rhombic Triacontahedron, also known as Kepler’s Solid, which is an example of a zonohedron.
Here are the pages and posts on this website that refer to SGDS; enjoy! 🙂
Last, but not least, I’m copying the content from a personal blog post (from a decade ago) which provides details on many of the images in SGDS, including how to draw many of the 2-D patterns (which took the form of an email Q and A response):
(Question)
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.
(Answer)
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 photocopied 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 Resources page, 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 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 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 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!
Cross symbolism, coloring books for adults, vesica piscis and misc. links
I recently received this inquiry about the symbolic meaning of a cross:
Hi, I love your site. I am learning so much. I don’t see any information about the symbol ‘The Cross’. Is the cross a universal symbol? A sacred symbol? It’s the symbol used in Christianity but does it have wider significance?
Thank you for your time and your knowledge! Thank you, thank you,
– A., California
… and I provided this response:
Thanks for the kind words, and your question.
Yes, the cross can represent a very wide array of symbolic meanings, and its obvious geometric aspects attest to its universality beyond any specific religious or philosophical adoption, but I try to remember that symbolic systems can be simplified to just 2 thought systems:
Inclusion: whatever leads us back to thoughts of sameness, interconnectedness and ultimately Oneness
and
Exclusion: whatever leads us deeper into the metaphoric darkness of separate interests, differences and identification with the ephemeral, dualistic and divisive.Therefore, seen from the former thought system of Inclusion, a cross can be a reminder that we can find the center (intersection) point where we transcend polarities, find common ground and respond with kindness … or an idol for specialness and ‘win-lose’ tug-of-war battles. It’s always our choice. 🙂
I touch on this symbolism in the chapter on the Law of Polarity in my second book, The Geometry Code: Universal Symbolic Mirrors of Natural Laws Within Us; Friendly Reminders of Inclusion to Forgive the Dreamer of Separation
You might also enjoy listening to this related recent conversation about the Law of Polarity.
Thanks again for your inquiry and support! 🙂
I keep finding more indications that the interest in adult coloring books is continuing to rise, such as this Coloring Book Master Class promotion. In addition to the classic reference book that contains over 1300 images suitable for easy photocopying for geometric coloring book use, my German publisher recently released a beautiful hardbound book (with a very nice subset of the images in the larger book) as Bewusst malen – Heilige Geometrie which also has some great quotes on facing pages. Thanks again to fellow author and artist, Jay Goldner, for his work in bringing this second book containing my geometric artwork to Europe and the world.
Here are a few miscellaneous links about sacred geometry and related, interconnected topics that have crossed (pun intended) my path recently that you might find interesting:
- Sacred Geometry Book Design with Sacred Geometry Vector Set Vol. 1, 2 and 3
- Ascension Art – Designs by DavidDiamondheart
- Sacred Geometry Web with 3Dmandalas … be sure to also check out iConnect by MetaForms for similar 3D geometric designs
- Interview about *LLND and Sacred Geometry in their latest performance titled Cosmic Resonance
- Shutterstock: Collection of elements, symbols and schemes of physics, chemistry and sacred geometry
- Ted Talk: Golden Ratio Fibonacci Sequence TEDxEast: Matthew Cross
- I’m sure I’ve shared this before, but what a great cosmic example of the vesica piscis (the Hourglass Nebula) … to tie into the first topic (the shape of a cross) – if you draw a cross bisecting a vesica piscis shape, the ratio is the square root of 3 (√3), which is also the ratio of the diagonal across any two opposite corners of a cube and any edge side length.
- GeometryCode – Favorite Movies, Books, Music, Software, and much more…
Geometric art and mandalas du jour
From the ‘elegant fun’ department: these kinetic sculptures by David C. Roy remind me simultaneously of favorite screen savers, animated crop circles and perhaps a few other moving mandala metaphors for cyclic interactions and relationships with curved arcs, circular and Yin/Yang archetypes; some lovely examples of moving geometry suitable for adorning one’s walls. His site has some engaging videos and other fun stuff on his blog.
More geometric art from artist Karen Carty in northern California … golden rectangles and spirals on large canvases
… and another gossamer golden ratio design of threadlike elements (found via a quick google search 🙂
GeometryCode bulletin – June 2015
(1) News, Events, Interviews, Workshops, Classes, Exhibits, Products, Articles, Tutorials
Vibration Station Conversation: Emoto, Cymatics, Mentalism, Polarity and more…
Dave Cohen (a.k.a. Davie Crockett) and I shared this conversation on 28 June 2015, on his LA Talk Radio show. We began with talking about the work of Masuru Emoto, Hans Jenny, quantum technology, mind (of course!) and migrated into a variety of geometric and metaphysical subjects; the usual fun whirlwind dialogue. Third eye dilation, anyone? 🙂
(2) Websites, Books, Videos, Imagery, Music and Quotes
- Fibonacci Sequence Animation video by Cristóbal Vila (with music by Wim Mertens) – Excellent animation of whirling squares (see image below), spirals morphing into a Chambered Nautilus, the Golden Ratio, the Golden Angle (137.507°) morphing into a sunflower head (see image above), dragonfly wings, and the hexagonal grid of an insects eye.
- Another article hinting (perhaps indirectly?) that mind might be the basis for our holographic dream of a cosmos: Some physicists believe we’re living in a giant hologram — and it’s not that far-fetched
- I recently (June 14, 2015) gave an audio visual presentation (via Skype) for Starr Fuentes’ 11th Annual Light Language Conference. My presentation was entitled “Metaphysics, Symbolism, Sacred Geometry and the The Geometry Code: Universal Symbolic Mirrors of Natural Laws Within Us; Friendly Reminders of Inclusion to Forgive the Dreamer of Separation.” Thanks to Starr for inviting me and Sean for his technical support. 🙂
(3) Request for Submissions
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.
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.