Pencil Polyhedra

After watching Little Man Tate, a movie about a child prodigy, I grabbed some pencils and elastics as he did and tried to make some geometric shapes. I made three of the five Platonic Solids;

the tetrahedron, with 6 pencils (edges) and 4 elastics (vertices),

Here's an 'imploded' version of the tetrahedron; the elastics have been moved much closer to the middle of the pencils.

the octahedron, with 12 pencils and 6 elastics,

and the icosahedron, with 30 pencils and 12 elastics.

The reason I only made 3 of the 5 platonic solids is because the other two are unstable. The icosahedron was very difficult while building, but once it was completed it was very stable. The cube on the other hand was frustrating the entire time. The dodecahedron was virtually impossible. This (in)stability has to do with the shapes of the faces. Notice that the three I made had all triangular faces. I explain this in detail here.

I tried to make a cube with hypotenuses as I mentioned. This has a few, but the pencil thickness starts becoming a large enough factor to cause distortion by itself. Also, the hypotenuse is longer than the edge, so I had to move the elastics closer to the middle of the pencils.

Lastly, I made some DNA. This is something I try with any modeling set I come across, e. g. Legos or Zome. The joint I used to attach here was a little ridiculous, but was the most stable thing I could come up with. It works perfectly fine if the DNA is infinitely long, otherwise you need to pull on it.


Overall this was very fun, and the first two structures were easy. Grab some pencils and elastics and see what you come up with.

-Alex Scott

Make a Doorstop

Back in the beginning of the school year I decided to make a doorstop. I had a design idea that was too simple not to construct. Forget wedges; this was going to be compression-based. My idea involved only three parts.

• compressible foam
• a hard square
• duct tape

It's a simple one-way mechanism. It seemed strange to me that I hadn’t seen the design before. Just apply a bit of planned duct tapping and it’s all set. Push the door far enough, and the foam does the work for you. When you want the door shut, just step on the plate. Voilà!


You can put some duct tape on the upper corners to avoid scraping. Within a few days multiple people on the floor had these in their rooms. It’s fun, easy, and helpful!

-Alex Scott

Binary Music

I've always enjoyed counting in binary on my fingers, where up means zero and down means one. For those of you unfamiliar with binary, the first few numbers look like this;

0 => 0

1 => 1

2 => 10

3 => 11

4 => 100

5 => 101

6 => 110

7 => 111

8 => 1000

9 => 1001

10 => 1010

ad infinitum. Notice that all the powers of two are a one followed by zeros.

One day while sitting at the piano I decided to see what it would sound like if I played the same thing; a key pressed down meant 1, and a key up meant 0. To my surprise, it was a half-decent song! Here is the sheet music done in Finale Notepad.

Here is the song rendered in piano.

You can download this mp3 here.


Here is the song rendered in pure sine waves.


You can download this mp3 here.

There are 3 main reasons this is a reasonably enjoyable song.

1. The first two digits provide the beat by cycling through 00, 01, 10, 11.
2. The highest digit provides a melody which gets higher at a decreasing rate. This causes tension, especially when the highest digit is playing a B for about half the song. Since the C, or tonic note, is right above B, your brain feels pulled toward it.
   
3. The chord "progression" created by the middle digits has a tendency to clear up as soon as things get cluttered. As you can see in the video, this is intrinsic to the nature of counting in binary. Moreover, the clearing up slows down as the song continues (eventually leading to a full mess of 01111111) which further contributes to the tension.

I decided to end with 10010101, giving a nice major chord, and more time after tension release than ending at 10000001.

-Alex Scott

M&M Pixels

What else would you do late at night with a big bag of M&Ms? Since I only had three colors (I ate the rest) I first built a hexagonal grid, just like pixels on a screen.

This perspective shows translational symmetry along same-color rows.

This perspective shows adjacent translational symmetry.


Next up, spirals; a two branch hexagonal spiral,


a four branch (though two color) square spiral,


a three branch hexagonal spiral,


and a six branch (though three color) hexagonal spiral. Notice the missing center!


Then I just mushed together the colored piles.


Third act: fractals! Sierpinski's triangle was the hardest thing, because it relies on a triangle grid, not a hexagonal one. This means that the circle M&M is taking the place of a triangle pixel, so the M&Ms couldn't be tangential to six others.

Here I add red M&Ms to the areas that would continue to gain iterations to make it clearer.


I didn't have enough M&Ms for many iterations of the next fractal, so I decided to make them decay as you go northeast.


1
11
21
1211
111221
312211

The famous "look-and-say" sequence, in M&Ms. Here I make as many complete rows as possible.


And here I truncate some rows to fill up the picture. I love how you can see clearly that the lines start to converge to a repeating pattern! This also happens on the right side, but I didn't have enough time to make a right-aligned one. Maybe next time!

-Alex Scott