2D Geometries

(1) News, Events, Interviews, Workshops, Classes, Exhibits, Products, Articles, Tutorials

(2) Websites, Books, Videos, Imagery, Music and Quotes

Here are this month’s handful of new websites and pages of interest to sacred geometry enthusiasts:

• Save 20% on Sacred Geometry Design SourceBook (SGDS) or other books, calendars, etc. Use coupon code VERNUM until March 31, 2013 11:59 PM.
• Art: Section of a Golden Ratio Fractal
• Here’s a google+ page entitled “Sacred Geometry: It’s everywhere.”
• The image above – that seems appropriate to welcome in spring – is a Wikipedia image of romanesco broccoli; a superb example of fractals in nature.
• Here’s a neat photo of what appears to be a crystal in the shape of a truncated tetrahedron (which. BTW, also defines, quite accurately, the orbital relationship between Neptune and Uranus) … and the illusory ‘virtual polyhedron’ which appears due to the optics of the form is an icosahedron.
• This page about Octahedral_geometry includes a 3-D ray-traced image “Dodecahedral Bubble” which I made several years ago that is actually 12-sided, rather than 8-sided geometry, but the rest are mostly octahedral.
• It’s always interesting to see how interconnectedness permeates everything our mind attends to … if we’re looking for it! :-) … The other day, I was helping a new web design client locate royalty-free images for her website (just select the last pull-down selector “usage rights:” and choose: “free to use or share”), and I wanted to try, with the aforementioned settings, google’s image search (using the camera icon in the search bar, instead of typing text) on one of the images she liked, so I first tried it on one of mine (the Dodecahedral Bubble image below) …
  
• … and seeing related (a.k.a. interconnected) search results led me to this cool Zometool bubble image …
• … from this “All things Dodecahedral” site which has a page with dodecahedral lamps (I made one years ago but not nearly as elegant as these), handbags, water towers, maps, mirrors, speakers and even cheese … which led to a neat free “Curved Spaces app” that runs on Mac and Windows” … and this lovely image of Dodecahedral Poincaré (curved) Space:
  
• … Here’s a related addendum (added after this page was emailed to subscribers on 29Mar2013) thanks to Sara Frucht of Kaleidoscapes who comments:
  “The dodecahedron picture reminds me of the video ‘Not Knot’ that came out about 25 years ago. It has to do with knot theory. In it, they fly through negatively curved 3-space tiled with dodecahedra (the curvature is such that the corners of the dodecahedra are right angles). I think what you have here is the same kind of tiling. (Here are the links to this interesting 2-part video: Not Knot-Part 1 … and Not Knot-Part 2 )Also, I had to mention that I have the exact same Steuben glass paperweight (with the icosahedron in the corner). I want to point out that it is not a perfect icosahedron – our space would have to be slightly positively curved for that to happen. (As you probably know) there is a tiling of positively curved 3-space with 600 regular tetrahedra (you could also think of it as a 600-sided 4-dimensional platonic solid). 20 tetrahedra meet at each vertex.”
• … and then there’s this interesting-looking “Sacred Geometry Explained” video course, which features a few familiar names like John Martineau and Robert Schoch. We had the privilege of hearing Schoch’s colleague, John Anthony West in 1992 at the Mena House – across from the Great Pyramid in Egypt – talk about his clever approach of getting an honest appraisal of the true age of the Sphinx – by masking off any distinguishing features and then asking Schoch to date the photo as a geologist, not an antiquities expert. You can probably guess that Schoch dated it quite a bit older than is generally assumed, since the water erosion he saw on this relic pre-dated dynastic Egypt by many millennia.) The “Sacred Geometry Explained” site also has audio (podcast) interviews about Freemasonry, etc. which was another ‘past life’ of mine in the early 1980s going through the “Blue Lodge” in Georgetown, Calif. where my interest in symbolism was given a big boost (and met a lot of friends.) … We’re all kin and connected! :-)