Off-Center Mandala
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Category Archives: Mathematics
Snowflake in Primary Colors
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Mandala Based on the Number 3
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If Recent Trends Continue, Gasoline Will Soon Be Free
Here’s what gas prices have done in the U.S. during the last three months:
The price of gas three months ago was $3.79 per gallon, and now it is $3.27, so, in three months, it dropped 52 cents per gallon. That’s a rate of -$2.08 per year per gallon, so, if this recent trend continues, gasoline will cost not much more than a dollar a gallon a year from now, and will become free sometime later in 2014. In fact, by the end of 2014 (again, if this trend continues), gasoline will have a negative price, which means they’ll pay us to take the stuff.
Sheryl Crow must have known this day would come, for she wrote a song about gasoline becoming free a few years back, which you can find below (embedded from YouTube) –– a song called, of course, “Gasoline.” Enjoy!
Golden Spectral Crystallization
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Created using Geometer’s Sketchpad and MS-Paint.
A Polyhedral Journey
So I wondered, what would happen if I took rhombic dodecahedra…
…and then affixed them to the sixty wider faces of a rhombic enneacontahedron?
Well, it turns out that this is what you get:
It’s at time like these — urgent situations in recreational mathematics — that I am most glad I bought Stella 4d, the program with which I made these images (and which you can try, for free, at http://www.software3d.com/stella.php). This would have taken months to figure out without the proper software! The next thing that occurred to me was to take the convex hull of the last polyhedron. That’s like draping a sheet around it and then pulling it tight. Here’s the result:
Stella owes its name, in part, to a complex operation involving extensions of edges into lines, or faces into planes, called stellation. Stellating the above figure gave me something I didn’t like, but stellating it again gave me this:
And then, after six more stellations, I arrived at the end of this particular polyhedral journey.
Polyhedral Helix
Mandala for the Number 45
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My First Polyhedral Tattoo
I love my latest tattoo. I designed the (uncolored) shape itself a year ago with software written by a friend in Australia, which you may see here: www.software3d.com/stella.php — and then a fantastic tattoo artist at Golden Lotus Tattoos in Sherwood, Arkansas (USA — with their website at www.goldenlotustattoos.com) made it even better. Nicholas Peirce does amazing work. This was a true team effort.
This is the 23rd stellation of the strombic hexacontahedron, which is dual to the rhombicosidodecahedron, one of the Archimedean solids.
I don’t want to have tattoos like those of anyone else, and I don’t think I have anything to worry about. =)
Stellating the Icosahedron
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I worked on this painting from 2002-2004, then, several years later, I gave it to two good friends of mine, when they married, as a wedding present. It is 16″ x 20,” and is painted with acrylics, on canvas. The painting was given its title because of its origin, as a colored (and slightly modified) version of the stellation pattern of the icosahedron.
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