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You are here: Home / Archives for 2D Geometries

2D Geometries

2023 Martineau Solar System Calendars available now

Friday, 23 September 2022 by Bruce Rawles

Once again this perennial calendar is available! These timeless images portray amazingly accurate geometric representations of the planetary orbits in our very own solar system – now available in printed calendar form with dates for 2023!

Martineau Solar System Calendars

Martineau solar system calendar -12 months

These 12 images are highly accurate geometric models of our solar system; details here. 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. A newly revised calendar (which is updated every year) with images from the Martineau Solar System is again available for 2022.

Filed Under: 2D Geometries, 3D Geometries, Archimedean Solids, Platonic Solids, polyhedra, sacred geometry art, sacred geometry calendars

High Resolution Imaging Science Experiment (HiRISE) camera photos

Sunday, 31 July 2022 by Bruce Rawles

I suppose one might say that these amazing images are more about geography than geometry, but I imagine that you might also notice that the abstract and seemingly amorphous shapes in these stunning images have some rather interesting geometric attributes, too! Some exhibit fractal patterns one might see flying over USA’s desert southwest and all show the profound intricacies of natural forces sculpting these desolate landscapes. These are all from NASA’s High-Resolution Imaging Science Experiment (HiRISE) camera on the surface of Mars. There are plenty of details on the NASA website that I won’t replicate here.

Of course, if you haven’t already checked out images from the newly celebrated James Web Space Telescope, check out those, too!

Mars: Martian Dust Devil Trails (NASA)

Mars: dunes (NASA)

Mars: dunes (NASA)

Mars: dark dunes (NASA)

Mars: carbon dioxide Ice - late summer (NASA)

Mars: dunes (NASA)

Mars: MRO orbiter banded wind ridges iapygia (NASA)

Thanks to fellow geometer, Dave Van Dyke – whose art, animation, and music I’ve featured on my personal blog – for alerting me to these artistic images from our cool, neighboring planet.

Filed Under: 2D Geometries, Fractal Geometry, sacred geometry art

Are Physics, Geometry and Science pointing to (Non-Dual) Metaphysics?

Tuesday, 28 June 2022 by Bruce Rawles

I just finished listening to an extended (almost 3 and half hour) fascinating podcast interview of cognitive scientist and author Donald Hoffman by Lex Fridman speaking on “Reality is an Illusion – How Evolution Hid the Truth” – (Here is a YouTube clip, evidently excerpted from the longer podcast.) If nerdy math and physics is over your head (as much of this was for me) you might want to skip to the last half hour or so where Hoffman delves into a more philosophical discussion with Fridman where more arcane subjects like Amplituhedron, Permutation matrices, Birkhoff polytopes and cosmological polytopes (new or minimally explored concepts to me) give way to a conversation that seems to lead one toward non-dual metaphysics (with which I’m much more familiar.) Here’s a related TEDtalk by Hoffman: Do we see reality as it is? I don’t pretend to understand much of the in-depth new math and physics that Hoffman talks about but I particularly appreciate his willingness to consider the idea that matter derives from consciousness and not necessarily the other way around! Here’s a quote that hopefully, I haven’t taken out of context: “The notion of self can be an artifact of projection…” (at about 2:16:39 into the podcast).

While doing some very preliminary perusals of some of the links above, I found a few interesting geometric links, including:

  • A 3D Printed Model of the Substructure of the Universe (the photo shows obvious icosahedral and dodecahedral symmetries)
  • The Golden Ratio and Us … and … Why is 1.61803399 considered a golden ratio?
  • … both the links above found from the Quantum Gravity Research site (which has a lovely polyhedra animation on the home page) and links to this nicely done video visually sharing the idea that the “20-group encodes 4-dimensional space” (from which the featured image for this post was derived.)
  • … and more in-depth physics here (The Einstein-Podolsky-Rosen Argument in Quantum Theory)

mirror-faced icosahedra descend on a city

 

 

Filed Under: 2D Geometries, 3D Geometries, 4D Geometries, modern physics, sacred geometry interviews, sacred geometry physics

Reflections on the Sacred: Geometry, Mind, Non-duality

Sunday, 5 June 2022 by Bruce Rawles

Over the years, I’ve been asked by many: “What Makes Sacred Geometry sacred?” to which I usually respond with something like this: Either everything is sacred … or nothing is sacred. While that terse response may seem to be evading the question, I’ve realized more and more deeply that it’s true, and if we gradually (with help from the Inner Inspiration we all can employ) shift our perception from the ephemeral to the eternal then our view of everyone and everything becomes kinder, more compassionate, tolerant and forgiving of the minutiae of the fleeting phantasms of form and the cosmically temporary. If truth doesn’t change, our task must be to seek and find what is true and cannot change; the laws of mathematics and geometry seem worthy candidates for possible means of finding the unalterably true. However, for something to be unequivocally true, it must apply to everyone and everything. The discipline of the scientific mind requires that we keep looking if we find exceptions to our postulates and theorems and persist until we find the safety, security, and serenity of what can never change. William Shakespeare penned lovely prose about the ideal of looking ever inward to the mind for what doesn’t alter or change when it (the mind) finds the alterable:

Sonnet 116: Let me not to the marriage of true minds
BY WILLIAM SHAKESPEARE

Let me not to the marriage of true minds
Admit impediments. Love is not love
Which alters when it alteration finds,
Or bends with the remover to remove.
O no! it is an ever-fixed mark
That looks on tempests and is never shaken;
It is the star to every wand’ring bark,
Whose worth’s unknown, although his height be taken.
Love’s not Time’s fool, though rosy lips and cheeks
Within his bending sickle’s compass come;
Love alters not with his brief hours and weeks,
But bears it out even to the edge of doom.
If this be error and upon me prov’d,
I never writ, nor no man ever lov’d. 

Seeking what is true for all, we realize we are all in the “same boat” either expressing kindness or in one way or another asking for it. Seen from this perspective, our true kinship – our real relationship – to everyone and everything merits kindness in response to expressions or requests for the same. That seems like a very serviceable and practical definition of sacredness – generalized to encompass all, sacredness reflects the perfection beyond the forms our senses and the mind’s machinery of interpretation seem to establish as real. We rarely question the vast number of assumptions we make every second about the world that seems vulgar and profane or at the very least disappointing in its impermanence.

A few dictionary definitions of the word sacred (most closely aligned with how I think of the word) are “revered, inviolable, inviolate, unimpeachable, invulnerable, untouchable, inalienable, protected, defended, secure, safe, and unthreatened.” These adjectives would suggest that nothing in this material world – where every form that appears eventually disappears – would qualify for sacredness; no exemption for the changed, changing, and changeable from decay, dissolution, and death. Yet while the laws of physics (particularly the Second Law of Thermodynamics) would suggest that nothing in spacetime is forever, we certainly can use our experiences in the world of space and time to guide us (even if largely as counterexamples) to find what is endless.

Our experience of sacredness – which I would equate with the purely innocent eternal nature of our being and all that remains in mind after we have completely forgiven ourselves and everyone for everything – depends completely on the thought system with which one views everything! If we look for what unites us, what is intrinsically the same for all – regardless of all the polarizing temporary attributes that seem to define our ephemeral personas and certainly our bodies – we find the sacred, innocent undifferentiated awareness from which all creation derives and to which we all belong.

What prompted this metaphysical musing? My computer calendar showed me that a decade ago today, I published my second book in print form, followed by a Kindle edition a few months later. I was also reflecting fondly on some related anniversaries:

  • 10 years ago today, The Geometry Code: Universal Symbolic Mirrors of Natural Laws Within Us; Friendly Reminders of Inclusion to Forgive the Dreamer of Separation became available in print
  • 15 years ago (2007), I “rediscovered” the pure non-dual metaphysics of A Course In Miracles by way of Gary Renard‘s first book: The Disappearance of the Universe: Straight Talk about Illusions, Past Lives, Religion, Sex, Politics, and the Miracles of Forgiveness and shortly thereafter started ACIMblog.com and started a weekly study group (now online)
  • 25 years ago (1997) I launched my first book, Sacred Geometry Design Sourcebook – Universal Dimensional Patterns
  • 30 years ago (1992), having “rediscovered” what has become known as sacred geometry via fellow mystical explorer and contemporary, Gregg Braden at a lecture in my mother’s living room in Livermore, California a year before – we (my now wife, Nancy, and I) accompanied Gregg (21 of us) to Egypt to explore the Great Pyramid of Giza and numerous sites up and down the Nile River
  • 50 years ago (1972) I graduated from Livermore High School

Thanks to all of you for many decades of support, collaboration, and shared enthusiasm for finding what is true! Here are some excerpts from the June 2012 bulletin that provide details about my second book, which combined interests in both sacred geometry and non-dual metaphysics. The book “The Geometry Code: Universal Symbolic Mirrors of Natural Laws Within Us; Friendly Reminders of Inclusion to Forgive the Dreamer of Separation became available 10 years ago today: on June 5, 2012.

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: Universal Symbolic Mirrors of Natural Laws Within Us; Friendly Reminders of Inclusion to Forgive the Dreamer of Separation by Bruce Rawles (logo) Learn more about The Geometry Code book
The Geometry Code: Universal Symbolic Mirrors of Natural Laws Within Us; Friendly Reminders of Inclusion to Forgive the Dreamer of Separation by Bruce Rawles (logo) Free sample chapter from The Geometry Code book with free bulletin subscription
The Geometry Code: Universal Symbolic Mirrors of Natural Laws Within Us; Friendly Reminders of Inclusion to Forgive the Dreamer of Separation by Bruce Rawles (logo) Preface by the author from The Geometry Code book
The Geometry Code: Universal Symbolic Mirrors of Natural Laws Within Us; Friendly Reminders of Inclusion to Forgive the Dreamer of Separation by Bruce Rawles (logo) Table of Contents from The Geometry Code book
The Geometry Code: Universal Symbolic Mirrors of Natural Laws Within Us; Friendly Reminders of Inclusion to Forgive the Dreamer of Separation by Bruce Rawles (logo) Acknowledgments for The Geometry Code book
The Geometry Code: Universal Symbolic Mirrors of Natural Laws Within Us; Friendly Reminders of Inclusion to Forgive the Dreamer of Separation by Bruce Rawles (logo) Endorsements for The Geometry Code book
Read more about The Geometry Code book, including an overview, the intended audience, and more.

About the book: The Geometry Code

While I was completing work on Sacred Geometry Design Sourcebook, (completed in 1997), I was already working on another book, which was ready on June 5th, 2012. Rather than reinvent the wheel, I think the Preface I wrote explains how the book came about and gives a good “big picture” of what it is about. I’ve uploaded the Table of Contents, Endorsements from friends and colleagues, Acknowledgments, a sample chapter, and more.

The Geometry Code book - Sample Chapter - Cover Page 1

Filed Under: 2D Geometries, Fractal Geometry, sacred geometry books, sacred geometry news

Geometric Inspiration and Education

Thursday, 21 April 2022 by Bruce Rawles

geometric art, color-filled intersections of simple 2D shapes shapesReflecting on the growth – explosion, really – of information available to us online compared to what we had access to just a few decades ago, I recalled that in the early 1970s when I was an undergraduate electrical engineering student at UC Davis, California, I used the card catalog in a long row of tidy wooden cabinets at the Shields Library – a building which covers an entire block of the campus – to look up everything I could find (at that time) on the Golden Ratio, Golden Number, Golden Section, Divine Proportion, Phi (ø) or Tau (τ) Proportion, Sacred Cut, Extreme and Mean Ratio, etc. and other synonyms for the ubiquitous (1 + √5)/2 ≈ 1.6180339887… value. This fascination was my response to a gift of two books – both with references to the golden ratio – from my mother who indirectly introduced me to this enthralling subject which later was popularized with the term “sacred geometry”:

  • Secrets of the Great Pyramid by Peter Tompkins
  • This Living Earth by David Cavagnaro

I found a few dozen books that led to other books and on and on into the mystical realms of the intersections of mathematics, ornamentation, art, music, architecture, history, and above all – mind. … But after checking out those books, I felt I had somewhat exhausted the more obvious references to this topic in this library. … Not anymore!

Fast forward a half-century; now googling Sacred Geometry, as of today (21 April 2022) we get a staggering 45 million results for this niche topic (including my evergreen minimalist GeometryCode Introduction to the subject now way past overdue for a revisit and update) and 481 million for the Golden Ratio!

The same curiosity still remains in my mind: What can be counted on that does NOT change? The laws of mathematics in general and geometry, in particular, seem relatively stable, fortunately, at least within the context of the Cartesian space-time paradigm. When I was in high school, I read Education and Ecstasy by George Leonard and I realized that to really dive deep and learn immersively, one needed to be motivated, inspired or at least have their curiosity seriously piqued or their assumptions about life challenged. Exploring some of the ideas that these readings opened up for me was enough!

Now there are a multitude of online offerings that can motivate young and old alike to explore esoteric topics like interconnectedness (e.g. quantum entanglement), geometric symbolism and synchronicities, and so much more. Another vital element that has a multiplying effect is FUN!

Here are a few quickly-found resources for educators and explorers in this realm (including teachers, home-schoolers) and philosophers of all stripes:

  • A simple but engaging animation showing basic 2D geometries morphing from one to another:
    Shapes – Learn 2D Geometric Shapes – The Kids’ Picture Show (Fun & Educational Learning Video)
  • 10 Geometric Art Explorations (Study measurement, area, fractions, and more!) … The graphic of color-filled intersections of simple 2D shapes on this page was adapted from the image below the “6. Frac-Geo-Bot” section on this page.
  • … for about 23 million more links, try googling “geometric art science toys videos”
  • or try these categories on the GeometryCode website: coloring books for adults, sacred geometry art, sacred geometry books, sacred geometry coloring books, sacred geometry toys … just for starters

Enjoy! :-)

Filed Under: 2D Geometries, 3D Geometries, coloring books for adults, Numbers and Proportions, sacred geometry art, sacred geometry coloring books, sacred geometry toys

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Unique, hard-to-find educational materials, toys and books such as Bradford Hansen-Smith's circle folding videos, books and supplies.

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