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2023 Martineau Solar System Calendars available now

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Once again this perennial calendar is available! These timeless images portray amazingly accurate geometric representations of the planetary orbits in our very own solar system – now available in printed calendar form with dates for 2023!

Martineau Solar System Calendars

Martineau solar system calendar -12 months

These 12 images are highly accurate geometric models of our solar system; details here. They were inspired by the remarkable work of John Martineau (publisher of Wooden Books), who wrote “A Little Book of Coincidence”. Tiled images of planetary surfaces and related images form the backgrounds. Images are two or more orbits defined by simple 2D (circles, triangles, squares, pentagons, hexagons, octagons) or 3D geometries (e.g. tetrahedron, icosahedron, dodecahedron) typically with 99.9% or greater accuracy. The work picks up where Johannes Kepler’s mystical exploration left off. A newly revised calendar (which is updated every year) with images from the Martineau Solar System is again available for 2022.

High Resolution Imaging Science Experiment (HiRISE) camera photos

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I suppose one might say that these amazing images are more about geography than geometry, but I imagine that you might also notice that the abstract and seemingly amorphous shapes in these stunning images have some rather interesting geometric attributes, too! Some exhibit fractal patterns one might see flying over USA’s desert southwest and all show the profound intricacies of natural forces sculpting these desolate landscapes. These are all from NASA’s High-Resolution Imaging Science Experiment (HiRISE) camera on the surface of Mars. There are plenty of details on the NASA website that I won’t replicate here.

Of course, if you haven’t already checked out images from the newly celebrated James Web Space Telescope, check out those, too!

Mars: Martian Dust Devil Trails (NASA)

Mars: dunes (NASA)

Mars: dunes (NASA)

Mars: dark dunes (NASA)

Mars: carbon dioxide Ice - late summer (NASA)

Mars: dunes (NASA)

Mars: MRO orbiter banded wind ridges iapygia (NASA)

Thanks to fellow geometer, Dave Van Dyke – whose art, animation, and music I’ve featured on my personal blog – for alerting me to these artistic images from our cool, neighboring planet.

TurboSquid 3D geometric models

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Fellow geometer, 3D animator, techno-nerd, mystic, and life-long friend, Dave Van Dyke alerted me to some examples of very cool 3-dimensional models using TurboSquid (3D Models for Professionals) a couple of days ago. The links below connect with a small set of the many examples of 3-d geometric models – some free, others inexpensive – all gems, especially considering the “labor of love” efforts put into these detailed models! Going beyond geometric constraints, you have orders of magnitude more to explore! They can be downloaded and adapted wherever your imagination might lead! Here are some samples to pique your interest!

Archimedean polyhedra permutations
Archimedean polyhedra permutations
polyhedron made of inter-locking blue squares
polyhedron made of inter-locking blue squares
geodesic polyhedra (truncated icosahedra); small and large sizes connected at vertices
geodesic polyhedra (truncated icosahedra); small and large sizes connected at vertices
polyhedron made of interlocking blue triangles
polyhedron made of inter-locking blue triangles
icosa-dodeca-geometric model with wavy extruded interconnecting struts
icosa-dodeca-geometric model with wavy extruded interconnecting struts

SMAs in SMA (SMA-ll stellated dodecahedra in San Miguel de Allende)

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¡Feliz Cinco de Mayo! Last week, my wife Nancy and I enjoyed a long-overdue, much-needed getaway/vacation and chose San Miguel de Allende, Mexico, a place we’d heard great things about for decades from numerous sources. We very much enjoyed our immersion into the culture, cuisine, and art that this historic city is known for. In addition to world-class dining, lots of “heart decor” and so much more, I was amazed at how many 3D geometric stars were present in this lovely city, both in numerous shops and even in permanent street art! Since artsy stars, wings, and hearts are here in abundance, there are plenty of stellated polyhedra, but the predominant variety seemed to be one of my favorite shapes, the small stellated dodecahedron (one of the four Kepler–Poinsot polyhedra) which I’ve featured in numerous places on this website. I mentioned (in my broken Spanish, resurrected from high school classes a half-century ago) to a few of the shopkeepers that a foldup version that would fit in a tourist’s suitcase might afford more sales, since shipping these lovely fabrications is probably a bit expensive.

If you want to make your own (I suggest trying in cardboard first) here’s a foldup pattern from page 219 of Sacred Geometry Design Sourcebook; you’ll want to make 6 copies of this page. Join the two edges labeled 1 and also join the two edges labeled 2. If you fold together just one copy of this page, you’ll get a double pentagonal pyramid, which is another interesting shape. However, if you fold up the 2 pentagonal pyramid halves, crease the middle shared edge, and fold the other direction, you’ll have 1/6 of what you need to make this classic shape. MC Escher fans will probably recall this classic image.

Small Stellated Dodecahedron fold-up pattern from page 219 of Sacred Geometry Design Sourcebook - Universal Dimensional Patterns by Bruce Rawles
Small Stellated Dodecahedron fold-up pattern from page 219 of Sacred Geometry Design Sourcebook – Universal Dimensional Patterns by Bruce Rawles

I’ve included an assortment of photos from this trip below, including a few other familiar geometries you’ll probably recognize; enjoy! For many more photos of our San Miguel de Allende, Mexico trip this past week, visit my personal Facebook page.

Small Stellated Dodecahedra hanging from the ceiling of the gazebo in the centro park adjacent to the Parrochia church, San Miguel de Allende, Mexico
Small Stellated Dodecahedra hanging from the ceiling of the gazebo in the Centro park adjacent to the Parrochia church, San Miguel de Allende, Mexico
cluster of brass Small Stellated Dodecahedra; San Miguel de Allende, Mexico
cluster of brass Small Stellated Dodecahedra; San Miguel de Allende, Mexico
Small Stellated Dodecahedra and many other colorful artsy decorative items in another street vendor shop; San Miguel de Allende, Mexico
Small Stellated Dodecahedra and many other colorful artsy decorative items in another street vendor shop; San Miguel de Allende, Mexico
Small Stellated Dodecahedron -hanging in a restaurant interior courtyard; San Miguel de Allende, Mexico
Small Stellated Dodecahedron -hanging in a restaurant interior courtyard; San Miguel de Allende, Mexico
street vendor photo: metal small stellated dodecahedra and other art objects; San Miguel de Allende, Mexico
street vendor photo: metal small stellated dodecahedra and other art objects; San Miguel de Allende, Mexico
metal stellated polyhedra decorating trees in an interior courtyard; San Miguel de Allende, Mexico
metal stellated polyhedra (one of many polyhedra) decorating trees in an interior courtyard; San Miguel de Allende, Mexico
metal stellated polyhedra; San Miguel de Allende, Mexico
metal stellated polyhedra; San Miguel de Allende, Mexico
interior of a metal stellated polyhedron; San Miguel de Allende, Mexico
interior of a metal stellated polyhedron; San Miguel de Allende, Mexico
metal stellated polyhedra; San Miguel de Allende, Mexico
metal stellated polyhedra; San Miguel de Allende, Mexico
Small Stellated Dodecahedra and other geometric lamps; street vendor lamp shop; San Miguel de Allende, Mexico
Small Stellated Dodecahedra and other geometric lamps; street vendor lamp shop; San Miguel de Allende, Mexico
large metal small stellated dodecahedron on street corner 1 block south of Parrochia church; San Miguel de Allende, Mexico
daytime photo of a large metal small stellated dodecahedron on the street corner one block south of Parrochia church, San Miguel de Allende, Mexico …
large metal small stellated dodecahedron casting light on the street corner at night; San Miguel de Allende, Mexico
… the same large metal small stellated dodecahedron casting light on the street corner at night; San Miguel de Allende, Mexico
courtyard art: large stellated cube; San Miguel de Allende, Mexico
courtyard art: large stellated cube; San Miguel de Allende, Mexico
reflecting sphere art in hotel lobby; San Miguel de Allende, Mexico
reflecting sphere art in a hotel lobby; San Miguel de Allende, Mexico

Other examples of small stellated dodecahedra from this website:

sculpture by Gregory Hoag of I-Connect (formerly Metaforms).

 

zometool stellated dodecahedron
zometool construction (the outer blue shape is a small stellated dodecahedron)

New Frontiers of the Gold Country - logo

 

Geometric Inspiration and Education

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geometric art, color-filled intersections of simple 2D shapes shapesReflecting on the growth – explosion, really – of information available to us online compared to what we had access to just a few decades ago, I recalled that in the early 1970s when I was an undergraduate electrical engineering student at UC Davis, California, I used the card catalog in a long row of tidy wooden cabinets at the Shields Library – a building which covers an entire block of the campus – to look up everything I could find (at that time) on the Golden Ratio, Golden Number, Golden Section, Divine Proportion, Phi (ø) or Tau (τ) Proportion, Sacred Cut, Extreme and Mean Ratio, etc. and other synonyms for the ubiquitous (1 + √5)/2 ≈ 1.6180339887… value. This fascination was my response to a gift of two books – both with references to the golden ratio – from my mother who indirectly introduced me to this enthralling subject which later was popularized with the term “sacred geometry”:

I found a few dozen books that led to other books and on and on into the mystical realms of the intersections of mathematics, ornamentation, art, music, architecture, history, and above all – mind. … But after checking out those books, I felt I had somewhat exhausted the more obvious references to this topic in this library. … Not anymore!

Fast forward a half-century; now googling Sacred Geometry, as of today (21 April 2022) we get a staggering 45 million results for this niche topic (including my evergreen minimalist GeometryCode Introduction to the subject now way past overdue for a revisit and update) and 481 million for the Golden Ratio!

The same curiosity still remains in my mind: What can be counted on that does NOT change? The laws of mathematics in general and geometry, in particular, seem relatively stable, fortunately, at least within the context of the Cartesian space-time paradigm. When I was in high school, I read Education and Ecstasy by George Leonard and I realized that to really dive deep and learn immersively, one needed to be motivated, inspired or at least have their curiosity seriously piqued or their assumptions about life challenged. Exploring some of the ideas that these readings opened up for me was enough!

Now there are a multitude of online offerings that can motivate young and old alike to explore esoteric topics like interconnectedness (e.g. quantum entanglement), geometric symbolism and synchronicities, and so much more. Another vital element that has a multiplying effect is FUN!

Here are a few quickly-found resources for educators and explorers in this realm (including teachers, home-schoolers) and philosophers of all stripes:

Enjoy! :-)