Sacred Geometry Media Resource Blog
I recently had an email inquiry (and then a follow-up technique) from a reader of Sacred Geometry Design Sourcebook about how to replicate the “Flower of Life – with Second Harmonic overlay” illustration on page 87 using classic straightedge and compass techniques. Here is her illustration, with comments. The basic technique is to subdivide the underlying hexagonal/equilateral triangle grid by the number of the harmonic desired. Thanks to SEEW from Maryland for the contribution!
Recently, I had the pleasure of visiting the Zometool factory in Longmont, Colorado.
There, my favorite (hands down!) geometric toy, er, I mean modeling system, is manufactured. Paul and Carlos gave me a tour of the amazing technology where these wonderful plastic components are made by the gazillions. The secret of the hub, rumor has it, is the trained microscopic radiolaria that already understand the necessary geometry and amazingly eat away the parts of the hub that don’t look Zome-ish. You’re not buying that idea? Oh well… maybe there’s more to it than that… :-)
The primary purpose of the day’s festivities was to begin assembling circular ‘rosettes’ (note the white quasi-circular shapes with 6 yellow hubs in some of the photos) to be further assembled into a new art piece for the Denver Art Museum. (Stay tuned for updates on the blog page.) Here are a few photos from the fun, collaborative day with great music provided by Paul’s daughter Lizzy, and excellent Zometool assembling fuel provided by Carlos and others. I’m looking forward to seeing the finished project at the Denver Art Museum! :-)
Zometool, with the addition of green struts, can build many of the designs – both 2 and 3 dimensional – that appear in the pages of Sacred Geometry Design Sourcebook (SGDS) and other 2D and 3D models. Now, more than ever, this superlative modeling system (which is also the coolest toy in the geometric Universe, in my opinion) is a fabulous complement to Sacred Geometry Design Sourcebook.
The green struts allow for square root of 2 proportions relative to blue struts, which allow shapes like tetrahedra, octahedra, star tetrahedra, several more Archimedean Solids and MUCH more to be built. Amazing how adding another proportional system to the prior version seems to add many dimensions to the possibilities. (BTW, the feline model within the model is Cooper, our new kitten.)
Here are examples of some of Zometool models that appear in the pages of Sacred Geometry Design Sourcebook. I’ll be adding to these as I go on, so look for announcements in the monthly bulletin about updates to this page. This example, from page 236, shows the 2-D projection of icosahedral and dodecahedral cross-sections, and the underlying golden rectangle and golden-ratio-based geometric proportions.
I recently started experimenting with Nanodots Magnetic Constructors (a 216 magnet set of remarkably strong (and fun!) little spherical (NdFeB) magnets. They are enjoyable to play with just from a tactile, sensory perspective, since they are like a set of high-tech micro-planets you can squeeze and morph in your hand like modeling clay … and the next moment, when you pull the amorphous mass apart, you get dynamic strings of metallic pearls that have amazing tenacity to maintain the connection to the whole. I’m just getting started in using Nanodots to explore my primary interest in geometric shapes.
Here are a few photos of Nanodots in 2D (flat shapes in a plane).
As you might imagine, if you make two shapes and put them close together on a flat surface, suddenly you find yourself with one shape! Symbolically, the magnetic principle abhors duality! :-) When you have smallish shapes in close proximity, but not so close that they join, you can rotate one and the neighboring shapes will rotate in tandem, almost like invisible gears; cool! :-)
I’ve made a few simple 3D geometries with Nanodots, but will need to spend more time and try a variety of polyhedra and other shapes. Interestingly, a few of the shapes (like the tetrahedron which moves immediately into a square and the octahedron which jumps into a more space-filling arrangement) are a bit tricky to hold (without some external constraint), since their geometries when made of magnetic spheres tend to fly apart and rearrange into more stable magnetic alliances. I think I see why the seasoned users make stable clusters and then make the larger shapes out of these smaller clusters.
Since their magnetic properties lend toward modeling with larger clusters that aren’t as influenced by smaller numbers of spheres, I’ll explore further with larger sets. Here are some excellent examples that others (mostly with larger sets than 216) have made.
Squishy Icosahedron Frame – YouTube
There are LOTS of great examples (both videos and static images) of polyhedra and other geometric shapes that are superb uses of Nanodots here; enjoy!
I’m giving a day-long, hands-on* sacred geometry workshop from 10AM-5PM on Saturday, October 8, 2011, here at our new home in Castle Rock, Colorado. We’re about 20-60 minutes south of Denver, depending on what part of the metropolitan area you might be driving from. Cost is on a sliding scale from $25-$75 based on need. Pre-registration is required, due to limited space around our dining room table! :-) Please contact Bruce via GeometryCode.com to register. I’ll be happy to phone or Skype with even more details. Please bring a geometer’s compass, straight-edge, scissors and cellophane tape; I will supply lots of 2D and 3D handouts including platonic solid fold-up patterns, plus LOTS of visual multimedia imagery, animation and more, along with plenty of theory on the mystical underpinnings of sacred geometry! :-) I typically bring most of my extensive library on the subject out for everyone to peruse; you can see most of them (except some of the rare and obscure titles) on the GeometryCode Amazon aStore. Here is a full resolution printable flyer for the event.