I made this using Stella 4d: Polyhedron Navigator. You may try this software, for free, at http://www.software3d.com/Stella.php.
A Transparent Rhombic Triacontahedron
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Monthly Archives: August 2016
The Compound of the Dodecahedron and the First Stellation of the Icosahedron
I made this using Stella 4d, available here.
A Transparent Rhombic Dodecahedron
Created using Stella 4d, a program available at this website: http://www.software3d.com/Stella.php.
A Music Video: Janis Joplin’s “Mercedes Benz”
“A song of great social and political import” from the 1960s, as well as a fun song for which to make a music video — or sing, a capella, in public, loudly and obnoxiously. =D
A Peek Backwards, as Far Back as Possible
Never before have I deliberately tried to recall my earliest memories. This morning, however, simply to see what might happen, I tried it. In my imagination, I returned to further back than I ever had gone before, to a period before I learned to communicate. In this early period, I could visualize things, with the imagery which appeared being geometric in nature. Later, I had to learn English, as a second language, to express the mathematical ideas in my head. My first word, according to my parents, described one of the two shining round things in the sky: “Moon.” I have always preferred moonlight to sunlight, for the intensity of direct sunlight is painful to me.
At least, that’s how I remember these things; I could be wrong about the earliest parts. All I know is that the image above popped into my head, when I tried to recall my oldest accessible memory. I then made the image above, in a short period of time, using Stella 4d, Polyhedron Navigator, available to try for free at this website. (I’ve used the program for over a decade, and find it an indispensable tool for geometrical investigations, such as this recreation of what I found in this morning’s early-memory-search.)
A Deck of Polyhedra
There are 52 rotating polyhedra below. Starting right now, 52 of anything can be called a “deck” of that thing. The derivation of this term is the the number of cards in a standard playing-card deck. The deck is the smaller “cousin” of the mole, or 6.02 x 10²³ of anything, from chemistry, as well as the “big brother” of the dozen, or twelve of anything. All three units are measures of specific quantities, and can be applied to any objects, at least in principle. One never encounters a mole of people because there aren’t that many of us, but a mole of people can still be imagined. The same thing applies to a deck of Earths.
This deck of virtual, rotating polyhedra was created using Stella 4d, a program you may purchase here. If you would like to see a larger image of any one of these polyhedra, simply click on it.
494 Circles, Each, Adorning Two Great Rhombcuboctahedra, with Different (Apparent) Levels of Anxiety
The design on each face of these great rhombcuboctahedra is made from 19 circles, and was created using both Geometer’s Sketchpad and MS-Paint. I then used a third program, Stella 4d (available here), to project this image on each of a great rhombcuboctahedron’s 26 faces, creating the image above.
If you watch carefully, you should notice an odd “jumping” effect on the red, octagonal faces in the polyhedron above, almost as if this polyhedron is suffering from an anxiety disorder, but trying to conceal it. Since I like that effect, I’m leaving it in the picture above, and then creating a new image, below, with no “jumpiness.” Bragging rights go to the first person who, in a comment to this post, figures out how I eliminated this anxiety-mimicking effect, and what caused it in the first place.
Your first hint is that no anti-anxiety medications were used. After all, these polyhedra do not have prescriptions for anything. How does one “calm down” an “anxious” great rhombcuboctahedron, then?
On a related note, it is amazing, to me, that simply writing about anxiety serves the purpose of reducing my own anxiety-levels. It is an effect I’ve noticed before, so I call it “therapeutic writing.” That helped me, as it has helped me before. (It is, of course, no substitute for getting therapy from a licensed therapist, and following that therapist.) However, therapeutic writing can’t explain how this “anxious polyhedron” was helped, for polyhedra can’t write.
For a second hint, see below.
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[Scroll down….]
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Second hint: the second image uses approximately twice as much memory-storage space as the first image used.
Nineteen Circles II
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One Possible Definition of Physics
With my metaphorical “mathematics of sets” hat on, this is what physics looks like, to me. The further you go in the field, the more challenging the mathematics gets; also, the better (and more expensive) the toys become.
A Music Video for “Ride Into the Sun,” by the Velvet Underground
This music video, for a Velvet Underground classic written by Lou Reed, John Cale, Sterling Morrison and Maureen Tucker, was made today — for a song originally recorded in 1969, the year after I was born. I used Windows Movie Maker to assemble it, and “painted” the preview-pic for the video, using MS-Paint. Other programs I used, for other images in the video, include Geometer’s Sketchpad, MS-Paint (again) and Stella 4d: Polyhedron Navigator. Of all these computer programs, my favorite is Stella 4d, which you may try for free at http://www.software3d.com/Stella.php.
RobertLovesPi.net 