There. Now, if I ever start an independent country, I’ll at least have a new flag ready.
I used three things to make this: Geometer’s Sketchpad (to make one black and white version; the whole thing is made of semicircles), MS-Paint (to color the six different versions which appear here), and the website http://www.makeagif.com (to assemble the six separate still images into one .gif file, with the illusion of motion). The surprising thing to me was how fast the process was, once I had the idea of my goal for a finished product.
It’s a mystery to me why this happens, but the parallels between different conversations which start with this question are simply amazing. First, I don’t get asked this question unless talking to a teenager . . . and then, nearly every time this happens, the rest of the conversation follows the same pattern.
First, I answer the question honestly, with a single word, by simply naming my favorite color.
After telling this one-word, five-letter truth, I then get a response which has become utterly predictable: “Black’s not a color!”
Even stranger: such inquisitions only seem to come from teenagers who are dressed in such a way as to let the following response work: “What color is your t-shirt?”
Sometimes they even look down at that point, presumably to check, which lets them see the answer to my question for themselves:
After that one question from me, for some reason, they tend not to say much more.
While the polyhedron above, informally known as the “soccer ball,” has icosidodecahedral symmetry, its coloring-scheme does not. Instead, I colored the faces in such a way that the coloring-scheme has pyritohedral symmetry — the symmetry of a standard volleyball. This rotating image was made with Stella 4d, a program you can buy, or try for free, right here: http://www.software3d.com/Stella.php.
RobertLovesPi’s social-interaction lesson of the day: different colors of fabric can actually mean something else, besides simply reflecting different wavelengths of light, and these meanings can shift quickly. (I already knew this could happen once per day, but was only just taught that this is also possible for n = 2, allowing me to extrapolate that, for the general case, n > -1, presumably with an upper limit set by the individual’s speed at changing clothes.)
As far as I can tell, n = 0 on weekends and legal holidays, in most cases, and n = 1 on most workdays (but not today, when the needed reflection-wavelength shifts from ~475 nm to ~550 nm after I leave the city of Sherwood, Arkansas, bound for a spot approximately 20 km South of there, in Little Rock, which is still in the same county).
Apparently my key to understanding this stuff is finding a way to analyze it mathematically. Also, posting such “new” discoveries to my blog increases the odds of me remembering them. However, unlike my last such finding (it involved chocolate chips not being a sandwich topping at Subway), I did NOT figure these things out “all by myself.” In fact, without help from two very important people, I doubt I ever would have figured them out at all!
The image above took very little time to make, online, at this website. The user interface there allows a large degree of control over the shapes and colors used in the images one produces. I didn’t notice a “save image” button, but that’s what screenshots are for, right?
This is the dual of the polyhedron seen as the second image in the last post on this blog. If colored differently, so that only parallel faces have the same color, it looks like this (click to enlarge):
I used Stella 4d to make these images, and you can find that program at http://www.software3d.com/Stella.php.