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!
Möbius strips of light … Donald in Mathmagic Land … Golden Ratio Nautilus
From the backlog of interesting sacred geometry links I’ve been meaning to share, here are three, with thanks to colleagues who shared the links with me so I can pass along to you! 🙂
- Möbius strips of light” … These mathematical structures show up everywhere from M.C. Escher drawings to electrical circuits, but almost never in nature. Now, a team of physicists have shown for the first time that light can be coaxed into a Möbius shape. …” Thanks to Ed Kellogg for emailing these links.
- Disney Cartoon From 1959 Teaches Sacred Geometry: ” … Donald in Mathmagic Land is a 27-minute educational film featuring the one and only Donald Duck. Released on June 26, 1959, it soon became the most popular educational film ever released by Disney. … ” If you haven’t seen this classic, you might want to watch it – or watch again – even if just for historical reasons; it’s an good very basic introduction (or re-introduction) to the the golden ratio, pentagram proportions, Pythagorean mysticism and a gateway to a more in-depth study of sacred geometry. Thanks to Haines Ely for this link suggestion.
- Golden Ratio Nautilus: George Hart clarifies common misconceptions about popular spiral shapes (specifically golden ratio spirals) in this interesting video where he sets the record straight … or is that curved? 🙂
New German Sacred Geometry Coloring Book for Adults! – Bewusst malen – Heilige Geometrie
Coloring Book for Adults … now available in a German edition!
A few months ago, I wrote that a new abridged version of the German edition of my first book Mandalas Der Heiligen Geometrie (MDHG) was underway. Mandalas Der Heiligen Geometrie (MDHG) is currently out of print, but I still have a few copies of this German edition of my Sacred Geometry Design Sourcebook (SGDS) available, if anyone in the US would like to buy one, just contact me if you’re interested in this collector’s item, which contains the original rainbow-colored cardboard fold-up Platonic Solid Mobile designed by the book’s translator, Jay Goldner, who graciously donated his time and effort to make the German version over a decade ago.
Now the new (abridged from the original MDHG) sacred geometry coloring book for adults, Bewusst malen – Heilige Geometrie, is available from the original publisher, Silbershnur Verlag. Here is where you can order a copy online. If you know anyone in Germany, please spread the word, thanks! And continued kudos and gratitude to Jay Goldner for his efforts is making these images available again, thanks to his collaborative efforts! 🙂
I have spent countless meditative hours over several decades exploring these fascinating patterns, both with compass and straightedge as classical geometers have done for millennia, and with modern CAD software to make the original Sacred Geometry Design Sourcebook (SGDS) from which this newest incarnation of that source material was derived. I hope you continue to find this practice as inspiring, relaxing, fun and mind-opening as I have over the years.
Use these links below to order the different versions of my adult coloring, reference and other books:
- Sacred Geometry Design Sourcebook (SGDS) – (English) over 1300 graphics, spiral-bound for easy photocopying with generous reference material and explanatory introductory text
- Mandalas Der Heiligen Geometrie (MDHG) – original German edition (currently out-of-print from the publisher, but contact me if you’re interested in one of the few remaining copies); includes a bonus mobile not in the English edition which suspends multicolored cardboard fold-up Platonic Solids; MDHG actually has all the same illustrations that SGDS has, PLUS the mobile!
- Bewusst malen – Heilige Geometrie – the new German coloring book for adults, excerpted from MDHG
- The Geometry Code: Universal Symbolic Mirrors of Natural Laws Within Us; Friendly Reminders of Inclusion to Forgive the Dreamer of Separation – (English) not a coloring book, and the geometry theme is more of a subtle backdrop in this book; a very different metaphysical treatise with humor, mysticism and practical application of ancient Hermetic Laws
Interesting geometric links to wrap up 2015
Hi all:
Here’s a fun and interesting collection of sacred geometry links you might enjoy:
- A hexagonal/cube/Flower Of Life (FOL) grid pattern on Shutterstock; also there this colorful spiral Flower Of Life overlay and some ‘seed of life’ cellular bubbles in a rectangular grid, plus another hexagonal grid idea with quasi-octahedral shapes framed by a non-regular hexagonal ‘chain’
- … and one more FOL grid idea and another Seed of Life/Hexagram pattern that almost looks like astronomical illumination due to the ‘shadows’ made by non-uniform edge color
- Speaking of seed of life (SOL) art, here’s a lovely Maori-inspired Seed of Life design
- Moving to classic sacred geometry from India, here’s a nice Sri Yantra design … and speaking of India…
- India Permits Free Energy Technology Despite Threats From UK, US, Saudi Arabia; I heard astronaut Brian O’Leary talk about Paramahamsa Tewari’s work decades ago at a talk he gave for our New Frontiers of the Gold Country group.
- Massless Particles Discovered, and They Could Revolutionize Electronics
- Continuing with a bit of physics – which never seems to venture far from geometric connections! – is this article: Physicists set quantum record by using photons to carry messages from electrons almost 2 kilometers apart
- Long-Lost Nikola Tesla Drawings Reveal Map To Multiplication
- So You Think We Are The Most Advanced Civilisation To Ever Inhabit This Planet? Think Again! and Everything We Have Been Taught About Our Origins Is A Lie. The aerial photo above shows the 8-sided geometry of the Great Pyramid at Giza, Egypt which was revealed in Peter Tompkins classic book, Secrets of the Great Pyramid, which also showed and discussed how the 4, 8 and 12-sided geometry (using both apothem side bisection and a smaller triangle at the bottom of the apothem on each face) accurately (and symbolically in terms of the rotational path of the earth around the sun mirrored by the pyramid’s circumference) depicts the solar, sidereal and anomalistic years in “pyramid inches.” Note that that latter definition which is defined by how long it takes the earth to return to the same place in it’s elliptical orbit, which is slowly rotating due to relativistic effects (if I recall Tompkins commentary correctly), so whoever built the Great Pyramid might have jumped the gun on Einstein’s discovery about earth’s elliptical orbit’s major axis shifting over time slowly!
- … and if you haven’t already got a wall (or desk) calendar for 2016 …
Every year I update this sacred geometry calendar which has images from the Martineau Solar System. Here are details about the 12 images which are highly accurate geometric models of pairs of planetary orbits in our solar system. They were inspired by the remarkable work of John Martineau (publisher of Wooden Books), who wrote “A Little Book of Coincidence.” Tiled images of planetary surfaces and related images form the backgrounds. Images are two or more orbits defined by simple 2D (circles, triangles, squares, pentagons, hexagons, octagons) or 3D geometries (e.g. tetrahedron, icosahedron, dodecahedron) typically with 99.9% or greater accuracy. The work picks up where Johannes Kepler’s mystical exploration left off.