When I was a child, I learned Roman numerals before I learned about the dollar sign. When I first encountered a dollar sign, I interpreted it as an “S” with a Roman numeral one superimposed over it. It then followed (I thought at the time) that the symbols for $2 through $10 would look like those shown above.
Fortunately, it didn’t take long before I figured out this would be impractical. I certainly would not want to have to write the symbol for $3,978, after all.
The image of two black spiders above is created by interference, and is an example of an interference pattern. The figures which are interfering are four points (and the rays which go with them), two close together on the right, and two close together on the left, but with the two pairs in different orientations. Each point has 240 rays emanating from it, and the rays are equidistant (in terms of angle measure), making each of these rays one euclid (1.5º) apart from its nearest neighbors.
First, Protostar:
In nature, protostars collapse under their own gravity until enough heat is generated to ignite nuclear fusion, at which point they become stars. The image above is my interpretation of a protostar, just before the moment it becomes a star. As for Star, my post-ignition interpretation, here it is:
While I did just make these images, they are simply inverted-color versions of images I made back in 2012, using Geometer’s Sketchpad. Here are the original-color versions (which I don’t like as much, myself), presented in a smaller size. You may enlarge either or both with clicks, if you wish.
I need two of these for my car — one for the rear bumper, and one for the front. I drive, on icy roads, about as well as the average Arkansan. This means I am proficient at sliding into ditches. It also means that, if our current weather forecast proves to be accurate, I’ll be staying home for at least the next 42 hours.
These are “lost mandalas” I found on an abandoned Tumblr-blog which I started before making my transition to WordPress. The first three were posted there in 2012, and the next two were posted in 2013.
I used Stella 4d to make the polyhedron above, and you can try this software for yourself here.
It is unlikely that anyone knows how many types of superstitious nonsense exist, for counting them would be an enormous task, with no compelling reason to do it, and only a slim hope of actually finding them all. However, a given person will be more likely than other people to know about a particular type — if it is related to things the first person finds of interest. For example, a physician will be more likely to be aware of homeopathy, and the faulty ideas upon which it is based, than would a randomly-selected college-educated adult.
It won’t take long, reading this blog, for anyone to figure out that I have a strong interest in geometry. Were it not for this, I likely would be unaware of another type of superstitious nonsense: “Sacred Geometry,” which I cannot bring myself to type without quotation marks. If you google that term, you’ll quickly find an amazing number of websites devoted to that topic, with many extraordinary claims about certain polygons and polyhedra, but you won’t find more than miniscule amounts of logical reasoning on any of these sites, mixed in with large portions of utter nonsense.
Geometry is inherently interesting, and many geometrical shapes and patterns are aesthetically pleasing. However, to search for their mystical or spiritual qualities is to do nothing more, nor less, than to waste one’s time.
I did not create, nor discover, the figure above, but found this picture at http://earthweareone.com/a-new-form-has-been-discovered-in-sacred-geometry-meet-the-chestahedron/. It is described there as a polyhedron with seven faces (well, they call them “sides,” but they clearly mean faces) of equal area — three faces with four sides each, and four faces with three sides each. Knowing that, I tried to figure out exactly what the back side of the figure would look like, but the text at that website isn’t particularly helpful in that regard, being filled with claims, allegedly related to this shape, regarding the human heart as an “organ of flow,” not a pump (What’s the difference?); “the earth in its foundational form [as] not a sphere but rather [with] its basis [being] a ‘kind of tetrahedron'” (What?); and a (claimed) special relationship between this polyhedron, and the oh-so-profoundly-mystical Platonic Solids. If none of that makes sense to you, you are not alone. It doesn’t make sense.
I often use software called Stella 4d (which you may try at http://www.software3d.com/Stella.php) to investigate the geometric properties of polyhedra. Based upon comments about this polyhedron written by Stella 4d‘s author, Robert Webb, I was able to create the rotating virtual model below, with Stella, to help me understand what all the faces of the green polyhedron above look like, included those on the back side, as the figure is shown in the picture above. This polyhedron is similar to an octahedron, with a single face augmented by a tetrahedron, and with three pairs of coplanar equilateral triangles then fused into rhombi. Here is that figure:
This isn’t the exact polyhedron in the first picture, but is isomorphic to it. Vertices and edges are moved a bit, changing the size and shapes of the four-sided faces, as well as the dihedral angles between the triangular faces, until all faces are equal in area. This process turns the three rhombic faces into kites.
On the above-linked “Earth We Are One” website, where the “sacred geometry” of this polyhedron is “explained” (and where I found the non-moving first picture here), this is called a “Chestahedron.” While Stella can help someone understand the geometrical properties of the Chestahedron, it offers no information whatsoever about the spiritual or mystical properties of this polyhedron, nor any other. There’s a good reason for this, though: the complete lack of evidence that any such properties exist, for the Chestahedron, or, indeed, for any geometrical figure.
As for the people, whom I’m calling the “Sacred Geometricians,” who are pouring so much time and effort into investigations of these alleged non-mathematical properties of hexagons, pentagons, enneagons, many polyhedra, and other geometrical figures, I have three things to say to them:
RobertLovesPi.net 