Platonic Solids

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

Martineau Solar System Geometries art exhibit in Castle Rock, CO

An exhibit of all 12 of my “Martineau Solar System” series framed giclées prints, plus 24 framed acrylic, collage and mixed media art images by Nancy Bolton-Rawles are now on display between May 7 and June 16, 2014 at the Philip S. Miller Public Library, 100 S. Wilcox St., Castle Rock, Colorado 80104 during regular library hours. This is the first public exhibit for either of us since we moved to Colorado almost 3 years ago… You can find upcoming, ongoing and past exhibits, classes and other events here. Enjoy! :-)

About the Martineau Solar System Geometries art and the Astronomical Geometry It Is Based On

The 12 images were inspired by the remarkable work of John Martineau, in his highly recommended book: “A Little Book of Coincidence.” The accuracy of his models is truly astonishing, typically 99.8 to 99.9% accurate. Johannes Kepler, who was fascinated with the idea of simple geometric models defining the planetary orbits, was on the right track, he just didn’t explore far enough… His original woodcuts appear below, showing the outer and inner solar system. He would have been thrilled to learn of Martineau’s models! I think John Martineau’s name will (some day, hopefully soon) be heralded among Kepler, Galileo, Newton and Einstein for the astronomical discoveries he’s made.

Here’s my image paying homage to Kepler’s elegant, though not particularly accurate models of the solar system.

All images in my “Martineau Solar System” series were created with the freeware ray tracing application, POV-Ray;  I’ve been using MegaPOV more recently. Here is an online gallery of this art (available as posters, greeting cards or apparel), plus other related images & photography.

More details about the individual images in the Martineau Solar System Geometries art exhibit

Here are early studies (sans NASA or other photographic tiled imagery for the background) for both the inner and outer solar system models, respectively, that John Martineau figured out; note that these highly accurate geometric approximations to planetary orbits averaged as circles (instead of the ellipses they actually are) were accomplished using only 2-dimensional geometric models, and rather simple ones at that! :-)

Outer Solar System: Solar System to Uranus Per Martineau

The background image for this foreground montage of John Martineau’s geometric solar system models is a tiled Kirlian photography image of fingertip corona discharge patterns that I took decades ago using a homebrew adaptation of a kit from Edmund Scientific Company.

Inner Solar System: Solar System to Mars Per Martineau

The background image for this closeup foreground montage of John Martineau’s geometric solar system models is a tiled color-inverted version of the Kirlian photography image used in the Outer Solar System model; the intent being to depict the warmer colors as a metaphor for the proximity to our sun.

Venus And Mars Per Martineau

With tiled planes of solar and lunar motifs in the background, a dodecahedron (12 pentagons, Plato’s symbol for ether or spirit) defines 20 spheres (the metallic looking ones) that exactly touch. Inside these are the orbit of Venus (green) and outside all is the orbit of Mars (faint red). The accuracy of the model (averaging the major and minor axes of the elliptical orbits) is 99.98%

Earth And Mars Per Martineau

With tiled planes of flora (a Hawaiian plant swirled within a honeycomb grid) and fauna (Chambered Nautilus) motifs in the background, an icosahedron (20 triangles, Plato’s symbol for water) defines 12 spheres that exactly touch. The centers of these define the orbit of Earth (blue) and outside all is the orbit of Mars (red). The accuracy of the model (averaging the major and minor axes of the elliptical orbits) is 99.9%

Earth And Venus Per Martineau

This image was inspired by the remarkable work of John Martineau, in A Little Book of Coincidence. Five tiled spiral galactic (NGC300) planes form the background. The perigee and apogee relationship between Earth and Venus is described by a nested pentagram pair. Accuracy is 99.9%

Venus and Earth Orbits Per Martineau

The orbital relationship between Earth and Venus is described by two concentric circles. The inner circle represents the orbit of Venus which passes through the centers of 8 circles that just touch each other. The outer circle represents the orbit of Earth which touches the outer sides of these 8 circles. The accuracy of this relationship is 99.99%

Earth and Mars Cross Per Martineau

This image was inspired by the illustration at the bottom of page 40 of the remarkable work of John Martineau, in A Little Book of Coincidence. A circle (Earth orbit) just touches each of 4 small circles, which in turn, each just touch 4 larger circles, which each touch the largest outer circle (Mars orbit). Spheres are used to represent the circles for artistic effect, and the outermost eight spheres are decorative only. The accuracy of this relationship is 99.9%

Venus And Mercury Per Martineau

Tiled, mirrored images of Mercury’s surface features (colorized three different ways) form the background. Three circles, whose centers are the vertices of an equilateral triangle, define an outer circle which exactly fits around the three (the orbit of Venus) and an inner circle which exactly touches the three vertices (the orbit of Mercury). Accuracy is 99.9%

Jupiter And Mars Per Martineau

This image was inspired by the remarkable work of John Martineau, in A Little Book of Coincidence. Tiled planes of Jupiters surface (top & bottom) and a colorized map of Mars sketched by the astronomer Antoniadi (left & right) form the background. The centers of four circles define the orbit of Jupiter and the orbit of Mars is defined by the red circle. The accuracy of this relationship is 99.99%

Jupiter, Saturn And Uranus Per Martineau

This image was inspired by the remarkable work of John Martineau, in A Little Book of Coincidence. Tiled, mirrored images of Saturns rings (colorized three different ways) form the background. Three concentric circles, define the orbits of Jupiter, Saturn and Uranus. The innermost (Jupiter) touches 8 middle points of an octagram. The outermost octagram points define Saturns orbit. The circle around an equilateral triangle around Saturn defines Uranus. The accuracy of the Jupiter/Saturn relationship is 99.9%

Jupiter And Earth Per Martineau

This image was inspired by the remarkable work of John Martineau, in A Little Book of Coincidence. Tiled colorized planes of the Great Red Spot of Jupiter (shifted +/- 120 degrees of hue, too!) form the background. The hexagon within a triple nested hexagram defines the orbit of Earth. The orbit of Jupiter is defined by the outer circle, and astonishingly, two clusters of asteroids (the Trojans) occupy Laplace Points, which are also defined by the + and – 60 degree positions in Jupiters orbit as shown on the diagram below. Accuracy of the Earth/Jupiter orbital relationship is 99.8%

Neptune And Uranus Per Martineau

This image was inspired by the remarkable work of John Martineau, after he wrote A Little Book of Coincidence (hence the model does not appear in that book.) Tiled images of Neptune’s surface line the union of two vesical tubes to form the background. A tetrahedron and its truncation define the orbits of Neptune and Uranus, respectively, with 99.93% accuracy. Here’s an early study (sans NASA tiled imagery for the background):

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

Here are a couple of geometric websites this month, with lots of interesting content for geometry enthusiasts:

• Geometric – a Pinterest site
• Sacred Geometries and Their Scientific Meanings – The Interface between Science and the Transcendental

(3) Request for Submissions

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

a Cube of One Way Mirrors

Reminiscent of Sara Frucht’s Kaliedoscapes which also explore the interplay of light reflected on the interior surfaces of polyhedra, both Platonic and Archimedean – see this recent related post about her reVERB™ Casual Music Game – this article about a cube with flexible walls made of one-way mirrors has a neat video showing what happens when the attached bellows change the geometry from flat planar surfaces. I’d like to see a ‘walk-through’ gallery of Kaleidoscapes that allow visual and acoustical interaction with all the Archimedean and Platonic solids as an interior participant.

New York City Sacred Geometry Fest

We already mentioned this event in the January 2014 bulletin, but there’s still time left (as far as I know) to attend a conference about sacred geometry – and these don’t happen that often – in New York next month. If anyone attends (I would, but have prior commitments) please feel free to send me any interesting links or reports from this fest … and say hi to our colleagues! Here’s a page of links from their site, and an example of one of the many workshops at this event: Leonardo’s Mind: The Geometry of the Renaissance.

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

Here are a few websites and links of interest to sacred geometry enthusiasts:

• Romanesco broccoli based-design anyone? This article explores shapes that may assist ecology, aesthetics and design.
• A fun video: Mathemusician Vi Hart Explains Space-Time with a Music Box and a Möbius Strip
• Thanks to my Mom for sending me this link with a lovely acoustic recording of cylindrical resonances: Singing Bowls for World Peace and Healing
• Organically geometric, this page of rock sculpture photography was from new age musician Iasos’ most recent bulletin.
• An interesting LinkedIn conversation (you can see where I chimed in) addressing “Do you know/use/ sacred geometry/golden ratio in your works?”
• Designer’s guide to the Golden Ratio
• “… I am trying to give people a sense of unity rather than build even more barriers.” says Mariam Nihal, author of an article entitled: Geometry key to Islamic art: Dana Awartani
• Ripples from the big bang? … Synchronistically, my niece is studying gravitational waves in space using laser interferometry.
• A Pinterest page: Geometric Inspired
• This designer uses a stellated octahedron a.k.a. star tetrahedron a.k.a. daVinci’s ‘stella octangula’ in her logo
• An article that explores Sacred Geometry and Unified Fields by MonkeyBuddha
• … and although it was a couple weeks ago (March 14), here’s a bit about The True Meaning of Pi Day … for fun

(3) Request for Submissions