"All This Math" by Naked Geometry There are two, 1st come, 1st serve.
"Nature uses only the longest threads to weave her patterns, so that each small piece of her fabric reveals the organization of the entire tapestry."
- Richard P. Feynman
some recent lasercut wood pendants by naked geometry
sacreddesign said: Hello, I was wondering if you could go a little deeper into debunking Metatron's Cube with regards to dodecahedra. The common methodology for producing one is distorted and incorrect, but I myself have managed to make it fit. From there, I have extrapolated icosahedra (as it is its dual) and a number of stellations with significant accuracy
It can be done in the 2nd way you describe, but the methodology that’s used isn’t particularly unique to metatron’s cube and is simply how one can construct it in any hexagon.
My deeper concern (while not an inaccuracy) is that the platonic solids that one creates from metatron’s cube have no particular volumetric correspondence to each other, which is why I prefer the sphere-packing approach as it has more correlation to nature. This is also why it doesn’t create “nested” platonic solids in any meaningful way, though that claim is tossed around a lot.
It’s a cool form, and does some cool things, but it requires too many jumpings through hoops to make elegant constructions, and is also seems to pick up new questionable powers every year. someone on facebook recently told me it answers every question ever asked, lol. :)
An artist in town, Alberto Almarza has a brilliant construction for the dodecahedron using only ruler and compass that I fully support, and corresponds more usefully (and accurately) to the other platonic solid constructions. I should record a video of him doing it sometime.
Does that answer your question? Thanks!
Metatron’s cube is somewhere in there
Metatron’s cube isn’t in here, actually. The hexagon shows some of the same alignments, but the lines here are more useful (in my experience as a geometer.) Metatron’s cube is a relatively recent figure popularized in the late 90s by a new age author. It’s pretty, but I don’t know any serious geometers who rely on it for constructions, it’s more hype than substance, in my experience. Here’s a little thing I wrote debunking the common myth that it somehow creates the platonic solids… Cheers!
There was some confusion in the thread my last facebook post, so I want to clarify a little bit about my opinion on the flower of life.
There is no question that, along with the vesica piscis, the golden rectangle & the pentagon, the flower of life is one of the most important structures in all of geometry. It is the beginning, literally, of almost all geometric design, including at least 50% of my work. It has been used by artists, architects & mathematicians for 1000s of years. One basically HAS to draw it to draw most other figures with a ruler & compass.
However, the nearly religious reverence given to it is relatively new. It was basically popularized in the 90s by the well-meaning but often inaccurate Drunvalo Melchizedek (here’s some good fact-checking by a very accomplished euclidean geometer of Drunvalo’s most popular book: http://thespiritscience.net/forum/viewtopic.php?f=60&t=6044&start=60#p172039.) While it appears in decorative motifs back into antiquity, it’s positioning now as a icon or idol worshiped on it’s own has little historical precedent.
I have no problem with people loving the shape, using it in their work, or even worshiping it. What I want people to recognize is that the reasons it was loved and used for 1000s of years is because of what it DOES… it’s practical usefulness for design, architecture, art & mathematics. It was always treated as a MEANS, not an END, and rightfully so. When we make something too concrete, we take away it’s flexibility, it’s brilliance! It’s like when Che Guevara became a t-shirt, and lost his meaning as a revolutionary.
This is the very essence of the zen quote of “If you see Buddha on the road, kill him." Buddha never wanted you to worship him, he only wanted to help you in discovering the essence of reality around us all… He was a MEANS, not an END… a verb, not a noun. A becoming…
So, by all means, make art that moves you, plunk the flower of life anywhere you feel it, and who cares how advanced you make it?! I started out very simply in my geometry.
But know that the power of the Flower of Life is best found by picking up a compass, drawing it, and then keeping exploring! Geometry is a living art, and there is more it will teach us.
The geometric masters of the past didn’t always stop with 7 circles, and neither should we. I’ll keep sharing new tricks I find, and look forward to seeing yours.
image: “Flower of Life Islamic Star Tiling” by Daud Sutton.
Daud’s awesome work is published by Wooden Books.
"When the power of love overcomes the love of power the world will know peace." - Jimi Hendrix
The flower of life nests at ~57.74% scaling and 30˚ rotation between layers.
An elegant derivation of the 1st 10 polygons from 9 circles. The pentagon requires additional lines to be accurately constructed, and the heptagon is impossible to accurately construct with ruler & compass. Play around!
Daniel Mirante (person in the image is Ben Woodward painting the glaze)
“I live on Earth at present, and I don’t know what I am. I know that I am not a category. I am not a thing — a noun. I seem to be a verb, an evolutionary process – an integral function of the universe.”
no. 1508 - Jonas Schmidt - www.isiope.com
sick. definitely enjoy this guys work, but this one is special.