Platonic Friends

The most useless math class I have ever taken was my seventh grade pre-algebra class. We’d usually show up to class and begin with about five minutes of taking notes. Extra difficult topics, such as multistep single variable algebraic manipulations like 2x+3=7 – you have to subtract three from both sides, and then also divide by two – may have taken ten minutes. After copying down the notes, we’d do half a dozen practice problems that all required the same steps to get the answer.

Then we’d get riddle worksheets. If you've never seen these, you've missed out. Basically, the answer to each problem corresponds to a letter. When you get all the letters, you put them in a certain order and spell out the answer to a riddle given at the top of the page. The riddles were almost universally terrible. Awful humor aside, the other problem with these worksheets was that since so many letters were needed, and each letter corresponded to a problem, each problem required the computational power of a broken abacus.

Compare this to college, where upon seeing that your math homework for the week is a single problem, you should get very, very suspicious. When you go look up the problem in the book, you find that it has twenty-seven parts that all build on each other, meaning that when you get the first part off by a few hundredths, by the time you finish you've concluded that after the soccer ball was kicked, it reached a maximum velocity of 2,793 miles per hour. Right . . .

So you go back to part one, where you read: A rocket is launched at an angle 37° to the vertical. It reaches escape velocity 3.492 minutes after liftoff. For the first 57 seconds, it has a variable acceleration of 17x+89.43, where x is the distance above the ground of the center of mass of the rocket in inches. The rocket is 1 meter long with an initial payload of 20 pounds. Each second, 0.748 pounds of fuel burns off. Assume the rocket is a cylinder with the fuel uniformly distributed in a smaller cylinder inside the rocket. . . . (Three pages later) Find the escape velocity of the rocket and what color it is.

Compare both of these to my tenth grade geometry class, which was neither as useless as pre-algebra nor as ridiculous as multivariable calculus, but still had a few quirks of its own. Foremost among those was my geometry teacher’s use of the overhead projector. By that, I don’t mean that she taught using PowerPoint slides from a projector mounted on the ceiling. She had one of those, but she preferred to use a 1950s projector with one of those super hot bulbs and an arm that had to be adjusted to focus the image. She would then project her transparencies (circa 1980) straight onto the board, which would then make a bright spot that would a) blind you and b) make it impossible to copy the notes from that spot.

All of this is to lead into my favorite geometry lesson. It has nothing to do with riddles, confusing homework, or even the overhead projector. It has everything to do with the five Platonic solids. Which, in case you were wondering, are the tetrahedron, hexahedron, octahedron, dodecahedron, and icosahedron.  (Platonic solids are polyhedrons with faces that are congruent convex polygons; the same number of faces have to meet at each vertex.)  As it happens, we have just enough of those magnetic bars and balls to make all five Platonic solids, with the dodecahedron stellated for structural reasons.

Clockwise from the large one: stellated dodecahedron, cube, tetrahedron,
octahedron, icosahedron

My personal favorite Platonic solid is the icosahedron. What makes my particular model even better is that

it glows in the dark.