||| ORCASIONAL MUSINGS BY STEVE HENIGSON |||
In order to graduate, Orcasian high-school seniors must create, and then successfully complete, a project that results in an improvement to the student, and improvement also to the school, to the island, to the environment, or to humanity in general.
Not least of this year’s improvements is a sculpture by Ewan Lister, by which he demonstrates an important set of mathematical, philosophical, and even historical concepts central to every student’s understanding of arithmetic, algebra, plane and solid geometry, and physics. Ewan is placing his interesting and instructive sculpture in Orcas High School’s Career and Technology Courtyard, near the room in which Physics is taught.
The sculpture displays the so-called Platonic Solids. These are five, three-dimensional shapes which meet the criteria proposed by the ancient Greek philosopher Plato as representing a sort of philosophical perfection. Each of the five shapes is a convex solid, and each is made up of a specific quantity of exactly congruent parts. Ewan went a little further in his presentation, doing a whole lot of extra and difficult calculation, and made his five examples all contain the same three-dimensional volume, as well.
The five Platonic Solids are: the Tetrahedron, a pyramid constructed of four congruent triangles (“tetra” is a Greek word for “four”); the Cube, with six square sides (so it could also be called the “exicohedron,” “exi” being Greek for “six”); the Octahedron, made of eight triangles (“octo” is “eight”); the Dodecahedron, made of 12 pentagons (“dodeka” is Greek for “12”); and the Icosahedron, made of (you guessed it) triangles again (and “ikosi” is Greek for “20”).
See and hear Ewan’s own, closely detailed story about his sculpture.Go HERE. Ewan’s is the first presentation in this group.
Learn more about the five Platonic Solids, including good illustrations.Go HERE. Some people believe that there is a sixth Platonic Solid, but even if Ewan agreed with them, he would find it impossible to include it in his sculpture. It cannot be built in the mere three dimensions allotted to us.
The sixth Platonic Solid is the Tesseract, which is a cube that has been extended into a fourth dimension. (“Tessera” is the Greek word for the cardinal number “four.”) Tesseracts are made of congruent parts, just like cubes, but instead of squares, Tesseract parts are themselves cubes, and there are eight of them.There is a clear explanation, plus illustrations, and even animations. Go HERE.
About 50 years ago, when I was making my living as a practicing leathersmith, a woman, a Professor of Mathematics at UCLA, came into my shop with a challenge: Make her a purse which would carry all of the accessories of her life, with each of the many, widely varied items in its own separate compartment, but the whole purse had to be markedly smaller than the one she carried with her at the time. After some amount of discussion, I accepted the job.
When she came back to collect and pay for her new purse, she was both pleased and confounded by the design work that my partner and I had done. We had completely accomplished her goal, and she wanted details about how we’d done it. Knowing her background, I told her that her new purse was actually a Tesseract, and that some of her necessities were being stashed “in the fourth dimension,” in order to make the purse a smaller size.
I also told her that there was a slight problem that we couldn’t seem to solve: If someone stuck a hand into her new purse, and thereby into the fourth dimension, the hand that came back out could have been modified by its inter-dimensional travel.
I know a trick of the fingers, by which I can make you believe that I have the usual 10 fingers, or sometimes 11, or, occasionally, only nine of them, and I demonstrated her purse while doing the finger trick. Both the purse and the prank were huge successes, and a really good laugh was had by all.
So about a week later, my partner and I found ourselves at the UCLA Mathematics Department’s Christmas party, showing off the purse, my finger trick, and the story that went with it all. And thereby I have direct proof that Mathematicians are pretty normal people, at least at parties, and that they appreciate well-presented mathematical pranks.
Ask Ewan why he didn’t include a Tesseract in his sculpture. You’ll probably get a laugh out of him.
Thank you for this, Steve. I’ve learned so many new things about you, reading your stories…thoughtful, entertaining and diverse. I think Ewan will be delighted too!
What a lovely surprise to read about the Platonic Solids in Orcas Issues. Thanks, Steve. One little correction, though: a cube is a hexahedron (the only regular hexahedron, in fact). The Greek word for six is ‘hexa’ (not ‘exi’ — there is a rough breathing mark in front of the epsilon, creating the ‘h’ sound), and there is no such thing as an ‘exicohedron’.
Marc: I learned to count in Greek, but only phonetically. I neither read nor speak Greek, other than a phrase or two, here and there.
The cardinal numbers that I know begin with “ena, dvia, tria, tessere, pende, exi, efta, octo…” So, to me, six is “exi,” and I constructed “exicohedron” all by myself, following the other four examples. Of course, I should have remembered “hexa…”
In response to your instructive correction, all I can say is, “efcharisto.”
Steve: Aha! You’re using modern Greek (which I don’t know), and I’m using Ancient Greek (which is what I know). So for all I know the rough breathing mark has disappeared from modern Greek. But the English names of the Platonic Solids all derive from Ancient Greek words.