sacred geometry videos

Monthly miscellany for mathematical musing

Sunday, 30 April 2023 by Bruce Rawles

Thanks to fellow geometer, James Barrett, for this interesting update about tiling patterns: Newly discovered ‘einstein’ shape can do something no other tile can do.
A portion of this Coast-to-Coast program is on crop circles, which have exhibited some amazing geometries for decades.
The Quantum Revolution (12 episodes): “Gaia is proud to present a comprehensive series from Nassim Haramein who offers a quantum revolution to the way we think about the universe, quantum mechanics, consciousness, and our spiritual connection.” Geometry and physics are inexorably linked! I attended one of Nassim’s fascinating all-day workshops a couple decades ago, give or take.
2022’s Biggest Breakthroughs in Math; one example: like 3D creatures able to discern situations that Flatlanders can fathom, sometimes we just need to add another dimension – in this case to solve a bubble problem.
Sacred Geometry circle art and some helpful how-to “Geometryptamine” construction videos by Zak Korvin.

$golden spirals from pentagram fractal by Geotryptamine$

Similar golden ratio, pentagram/pentagon, spiral constructions – with numerous variations! – are on pages 146-156 (among others) of Sacred Geometry Design Sourcebook.

Mirrored geometric solid cameo on new whodunit

Friday, 30 December 2022 by Bruce Rawles

Spoiler Alert: This post will reveal the Platonic Solid that stole the show (at least for me) on the latest flick by director Rian Johnson. If this isn’t an issue, read on! May I have the envelope, please…

I don’t often watch murder mysteries unless there’s a generous amount of tongue-in-cheek involved, such as my favorite classic of this genre, “Murder by Death” which I recommend if you haven’t seen it. The “22 Twain” punny address of the mansion at the beginning of that film had me hooked at the get-go.

Based on Johnson’s prior whodunit, we thought we’d give his new one a go, and enjoyed it, also. So… for silly fun, we recently watched (streamed at home) “Glass Onion: A Knives Out Mystery” which featured – in addition to the expected absurd assemblage of characters with a preposterous plot, and a fun puzzle box invitation featuring a “whirling squares” (Fibonacci) spiral, other familiar geometries plus assorted over-the-top glass sculptures in a billionaire island mansion with an infinity pool – a few witty pop-culture-for-nerds cameos like a Boston Dynamics “dog robot” porter and momentary dialogue about Google alerts – which I find helpful every week for feeding me news about sacred geometry and other metaphysical topics.

Regular readers will recall that this isn’t the first time I’ve featured the lovely geometric artwork of artist Anthony James … The (virtual envelope) contents of that award-winning geometric art (from my perspective) is … cue the drum roll … James’ Mirrored Icosahedron with the illuminated interior edges presenting the viewer with an exotic labyrinthine landscape of triangular tunnels. That’s it! At the focal point heart of the bulbish-shaped centerpiece glass onion sphere-like feature of the larger mansion sits a mirrored icosahedron which sure looks a lot like James’ handiwork! (If anyone knows any different, please let me know.)

The screen snap of a frame from the trailer doesn’t do it justice… Here’s a frame close-up from a video giving the “star” more exposure:

Speaking of mirrored and/or virtual polyhedra, see also: Sara Frucht’s Kaliedoscapes!

Alternate ending: If you were hoping for a dodecahedron, you might want to read this post on my other niche blog; the original model that appeared in the Lawrence Livermore Lab bulletin my Dad brought home early in the development of laser fusion showed a translucent plexiglass dodecahedron with 12 plexiglass cones centered on each pentagonal face all converging at a hydrogen pellet target.

Happy New Year all!

How to make a model of Nested Platonic Solids with Zometool

Monday, 29 November 2021 by Bruce Rawles

I recently disassembled a favorite Nested Platonic Solid model (for transport) and decided it might be helpful to take a few photos of the process and present them in reverse order, to help anyone wanting to use Zometool to build this unique geometric nest of the 5 regular polyhedra attributed to Plato. About a decade ago, I made this Infinite Recursive Animation of these Nested Platonic Solids and zoomed in for 3 full cycles of the loop to show the relationships between the five solids and some of the details that might be missed otherwise, so this post will complement that animation. Here’s a still frame from that animation that shows the 2 outermost polyhedra (the octahedron in light green and the icosahedron in dark blue):

frame from nested platonic solid animation showing octahedron-icosahedron golden-ratio vertex relationship — frame from nested platonic solid animation showing octahedron-icosahedron golden ratio vertex relationship

Here are all the Zometool struts and hubs you’ll need:

… and now we start by assembling the innermost polyhedron, the tetrahedron from these shorter green struts and white Zometool hubs:

green struts and hubs needed to make the outer octahedron: Nested Platonic Solids model using Zometool — green struts and hubs needed to make the inner tetrahedron model using Zometool

… adding the smaller blue struts and the ubiquitous white Zometool hubs to the green tetrahedron makes a blue cube (a.k.a. hexahedron); here we can see the √2 edge length proportion:

2 polyhedra; cube outermost - Nested Platonic Solids using Zometool — 2 polyhedra; cube outermost – Nested Platonic Solids using Zometool

Now adding these “roof caps” to each of the 6 square faces of the cube…

example of roof tents defining edges of dodecahedron outermost: Nested Platonic Solids model using Zometool

… we get a dodecahedron; see also page 229 in Sacred Geometry Design Sourcebook for an “exploded view” drawing in the lower-left corner of the page for additional reference.

3 polyhedra; dodecahedron outermost: Nested Platonic Solids model using Zometool

Now assemble 12 pentagonal pyramid caps …

pentagonal pyramidal caps making icosahedron: Nested Platonic Solids model using Zometool

… and attach to each of the 12 dodecahedron faces, to make it’s dual, the icosahedron:

4 polyhedra; Icosahedron outermost: Nested Platonic Solids model using Zometool

Finally, make these asymmetrical structures (with golden ratio prorportions) from the 2 larger sizes of green struts…

… and attach these to the icosahedron vertices to complete the outermost polyhedron, the octahedron:

All Five Polyhedra - Octahedron outermost: Nested Platonic Solids model using Zometool; note the golden ratio division of octahedral edges defining icosahedron vertices — All Five Polyhedra – Octahedron outermost: Nested Platonic Solids model using Zometool; note the golden ratio division of octahedral edges defining icosahedron vertices

Enjoy! :-)

Kinetic Geometric Art

Thursday, 6 May 2021 by Bruce Rawles

The dimension of time coupled with the other three spatial dimensions can add tremendously to the potential of geometric art as exemplified in these kinetic sculptures. We first looked at David C. Roy’s kinetic sculptures a few years ago, and this video provides an enjoyable update on his mesmerizing moving mandalas… and other kinetic art which leverages lots of talents including geometric sensibilities.

Moving further into full 3-dimensional kinetic art, here are more lovely examples of moving geometric art by artist Ivan Black. Among many other exquisite designs in this video, if you always wanted to see the (Fibonacci Spiral) “Whirling Squares” animated in 3D, check out this outdoor, wind-driven yellow sculpture which starts about 9:17 through about 10:03 into the video; gives new vitality to the “whirling” adjective! :-)

… and in case you missed it (or would like to be wowed again), here’s a link to a prior post from this site that links to Blooms: Phi-Based Strobe Animated Sculptures that heterodyne rhythmically in dazzling fashion, benefitting from the use of stroboscopic light applied to rotating forms with golden ratio proportions.

Sketches in Code: Randomness and Patterns in Science and Art – Livermore, CA exhibit

Wednesday, 28 April 2021 by Bruce Rawles

While visiting my hometown of Livermore, California this month, I was fortunate to see a very well done exhibit in the lobby of the Bankhead Theater entitled “Sketches in Code: Randomness and Patterns in Science and Art” which featured several interactive exhibits as well as numerous examples of 2D and 3D art, many of which will be familiar to those of us who have studied these realms for decades. Here is the detail from the Livermore Arts website:

Science, math, computers and art meet nature Explore how the intersection of mathematics, science, art and computers can be used to visualize and create artistic pieces which also describe and explain nature. As you tour this exhibit, we hope you see that, while art has often been described as an opposing discipline to mathematics, science and computers, in many ways they are very similar. In the end, all are creative processes that involve a journey of discovery. This exhibit is co-sponsored by Livermore Arts and Quest Science Center Bankhead Theater Gallery Feb 12–May 2 Open Fridays 2-6pm; Sat and Sun 1-5pm Limited entry, masks required. Family-friendly interactive exhibits with Covid protocols in place. Join us for this (exhibit) of science-meets-art.

If you’re reading this before May 2, 2021, you may still have time to see the exhibit in person if you’re in the San Francisco Bay area; recommended for the entire spectrum of those completely unfamiliar with the subject to those well-versed. Here are some cell phone photos of the exhibit items (most self-explanatory):

The first two photos are of a particularly nice 3D printed Sierpinski Tetrahedron (fractal tetrahedron) at the top of this article, with the second photo being a fun interior view with a pentagram-like interior contour:

If you’d like to make a Sierpinski Tetrahedron – a great geometry classroom or home school project! – here’s a fun sped-up how to video: (which also demos the same idea for a Menger Sponge.

$examples of fractals$

$fractal examples$

$fractal branching$