2D Geometries

Martineau Solar System Calendars again available; still 9 months left in 2022!

Friday, 1 April 2022 by Bruce Rawles

OK, I’m a bit late (by about 4 months from when I usually update these), but there are still nine months left in the year 2022 to enjoy these lovely calendars! Freshly updated, these timeless images that portray amazingly accurate geometric representations of the planetary orbits in our very own solar system are now (again) available in printed calendar form!

Martineau Solar System Calendars

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.

Educational Books and Toys: RedHen Update!

Tuesday, 28 December 2021 by Bruce Rawles

It’s been a while since we featured RedHen Books and Toys with their unique assortment of hard-to-find educational materials, toys, games, and books such as Bradford Hansen-Smith’s circle folding videos, books, and supplies, Zometool, Froebel gifts, and much more! For math or geometry teachers, homeschoolers, or anyone enthused about the study and practice of geometry – or wanting to propagate that enthusiasm – Red Hen has an excellent selection for kids spanning a wide age range.

To get a sense of the generous variety of available products, I would suggest clicking on the “All Items” link in the Red Hen website left sidebar, and then scrolling through a page at a time to not miss any of the unique and interesting items; the samples below are just a small handful of what you’ll find! Here are a few of the many unique items that make great gifts or educational catalysts year-round. I’m a huge fan of Zometool! Spirograph was a big positive influence in my childhood a half-century ago, so I’ll feature those two first. Enjoy!

Zome Crystallography kit

Spirograph Design Tin Set

Geometric Coloring Cards

Kaleidograph Flora

Rolligo

Mathematics with Geoshapes

Archimedes Square Stomachion puzzle

Fold a Soccer Ball

Tetrahedron Octahedron Cube poster

Golden Mean Calipers revisited

Sunday, 29 August 2021 by Bruce Rawles

From about 4:25 – 5:19 in this video, fine art instructor Ken Campbell reveals one of his 6 keys to designing great art – using the golden mean a.k.a. golden ratio a.k.a. sacred cut a.k.a phi proportion ≈ 1.618 (or its inverse which is roughly 62% – close enough for most small art projects – in laying out design concepts.

The ratio of AB to BC in the illustration below is in golden ratio proportion. (This “Dividing a Line by the Golden Ratio” illustration is from page 156 of Sacred Geometry Design Sourcebook – Universal Dimensional Patterns. That page also shows – with simple step by step instructions – how to make a golden rectangle (a more familiar classic construction, perhaps) using only a straightedge and compass:

I was working on another project in the office when I overheard these comments in the fine art YouTube video noted above that my wife, Nancy, was watching as she brushes up (pun intended) on techniques. I reminded her that my golden ratio compass was available for her art toolkit. The one I purchased a couple of decades ago (from Now and Zen of Boulder, Colorado, (c) 1997) appears to be no longer available, and the one I featured last year seems to be currently unavailable.

However, here are a few variations of golden ratio calipers that should work well. A couple of them also have an arm that locates the midpoint of the smaller length, and in the metal one, that additional arm’s location is reversible, so it can locate the midpoint of the longer length.

If you have artwork (2D, 3D or whatever) inspired by sacred geometry, and particularly that uses the phi (golden ratio) proportion that you’d like me to consider featuring on this site, please contact me! I enjoy sharing creativity from a wide range of media and artistic styles.

Fractal flotilla? Topological temple? Self-similar shrine? Growing options for fractal art

Monday, 28 June 2021 by Bruce Rawles

$IMception: fractal flotilla?$

This intriguing image is among those featured in this article about a Kickstarter campaign – by Raksha Singla, creator of IMception, a new project which aims to add a newcomer to the existing field of fractal generation software:

“This exciting new program on Kickstarter is a gateway for an eternal journey into the world of fractal illustrations. It is so simple to use that anyone can instantly become a confident artist.”

Here’s a related article with some current options for making your own fractal artistry: Ultimate Guide to Fractal Generators: The Best Fractal Software in 2021 (Free & Paid)

Here are numerous prior posts on the GeometryCode website that reference fractals.

Kinetic Geometric Art

Thursday, 6 May 2021 by Bruce Rawles

The dimension of time coupled with the other three spatial dimensions can add tremendously to the potential of geometric art as exemplified in these kinetic sculptures. We first looked at David C. Roy’s kinetic sculptures a few years ago, and this video provides an enjoyable update on his mesmerizing moving mandalas… and other kinetic art which leverages lots of talents including geometric sensibilities.

Moving further into full 3-dimensional kinetic art, here are more lovely examples of moving geometric art by artist Ivan Black. Among many other exquisite designs in this video, if you always wanted to see the (Fibonacci Spiral) “Whirling Squares” animated in 3D, check out this outdoor, wind-driven yellow sculpture which starts about 9:17 through about 10:03 into the video; gives new vitality to the “whirling” adjective! :-)

… and in case you missed it (or would like to be wowed again), here’s a link to a prior post from this site that links to Blooms: Phi-Based Strobe Animated Sculptures that heterodyne rhythmically in dazzling fashion, benefitting from the use of stroboscopic light applied to rotating forms with golden ratio proportions.