Designs Nobody Needs

I'm still trying to get facile with designing things for my 3D printer. I had a brief flurry of activity when I attended a workshop (thank you Math for America and Dr. George Hart). At that time I was using Mathematica, and exporting 3D plots. But my license for Mathematica expired, and I can't afford to renew it.

So I've been playing with a free tool, TinkerCAD. They have a library of some basic shapes, and if you fiddle enough with the graphic interface, you can figure out how to edit the shapes. Having attended another workshop recently where we explored Soma cube puzzles, I decided to try to make a design to print a plastic set of Soma cubes.

It's not particularly hard. Cubes are in the basic library of shapes on TinkerCAD. The only thing that took a little while to figure out is how to move an element of my design in the z-axis, since three of the basic pieces are more than one cube unit high. I made my design in two drawings: one of the four single height pieces (big L, little L, T, and Zed); and another of the three double height pieces (right chiral, left chiral, and corner).

TinkerCAD can export to .stl format, which Makerbot Desktop can open and export to .x3g for my printer. I was so proud of myself, I was about to upload the designs to thingiverse. But before doing that, I did a search. Some 48 other Soma cube designs are already up there. Nobody needs mine. But I'm happy I made it. Some day I'll even try printing it and see if it really works.

*** edit 20 Dec 2015 ***
I tried printing, and it didn't work out so good. I think my printer (Makerbot Replicator 2) may be introducing some errors in the z-axis towards the edges of the printing space. The parts more towards the center were fine, but the one furthest out had a sort of curved upper face, where it should have been completely level.

So I tweaked my designs to put just one piece per design, total of seven drawings. I'll give these a try later on today.

*** edit 22 Dec 2015 ***
My "one design per print job" drawings are printing out just fine. But I think the real problem was that the blue tape on my build plate was not sticking securely, and that introduced some waves into the build.

*** edit 5 Jan 2016 ***
An acquaintance asked for the files, so I did upload to thingiverse. Also added pictures to this post.

Soma Puzzle

Episode Three of the George Hart workshop at Math for America.

Given a supply of wooden cubes, how many shapes can you make by combining cubes such that 1) you cannot use more than four cubes, 2) rectangular prisms are not allowed, and 3) faces of cubes must match completely (no halfway or other fractional meetings). Turns out there are exactly seven different shapes.

So, if you glue the wooden cubes together into these shapes, and count them up, you have used exactly 27 cubes. By coincidence, 3^3 is 27. Can you arrange these shapes into a cube?

Yes, you can. Apparently there was a product sold decades ago called a Soma cube. It makes an interesting exploration into 3D geometric transformations. You can make the same pieces from correctly dimensioned cardboard boxes.

But you aren't limited to just a cube shape. You can make a snake, or a doggy, a dinosaur, and other shapes. Providing hours of exploration, all for a few dollars in materials.

Paper Construction from George Hart

I've been participating in a series of workshops with George Hart www.georgehart.com, and saw the activity described here at one of the workshop sessions. I tried it yesterday in one of my less-structured classes.

Overview: Students piece together twenty slotted equilateral triangles cut from card stock to make a ball. Here's what the ball looks like:

There are a few interesting things about this construction, and depending on time the facilitator can reveal these things more or less gradually. I didn't have confidence in my students' attention span, and so started on the multi-color construction.

I printed the templates on five colors of Wasau Astrobrights cardstock. Construction calls for four triangles of each color. The template prints eight to a sheet, so I precut them into halves. Students had to further cut into triangles and cut the slots. The slots are how the triangles are pieced together.

Next, students need to explore and figure out how the triangles slide together to form a stable shape. Prompts are: make a natural structure with the triangles, use the slots, structure should be three-dimensional, pieces should not be bent or folded, structure should be symmetric, and should use all twenty triangles.

Here's an example of the basic shape. Notice that five triangles combine to form a pentagonal hole.

Once students have this basic shape, it's a matter of extending around in a ball.

Once they built the ball, I then asked them to take it apart and rebuild it. This time they should make sure each pentagonal hole was surrounded by each of the five colors. About half the class was unwilling to do this. But the other half accepted the challenge and accomplished it, one staying after the bell to complete her project.

Some interesting things: A cube is visible embedded in the ball. There appear to be only four unique ways to assemble the ball with five colors to a pentagonal hole. The figure can be thought of as an icosahedron whose faces are rotated. Positioning five colors around a hole gives to opportunity to discuss permutations involving circles.

Hyperboloids from Bamboo Skewers

I was fortunate to have a visit today from Dr. George Hart (sponsored by Math for America). George led students in an activity building hyperboloids from barbecue skewers and hair rubber bands. I combined my AP Calculus BC students with a colleague's AP Statistics students for this double-period workshop.

First George explained some of the basic geometry of hyperboloids. One interesting thing in particular is that, while the surface of the hyperboloid is what we would normally call "curved," each point on the surface is the intersection of two straight lines.

The plan was to model a subset of the surface using bamboo skewers. For the model to work, we had to keep a regular pattern of "in front" and "behind." George explained this.

Basic plan was to pair skewers in the middle with a rubber band. Then we would attach pairs of adjacent ends. All the while we must maintain the "in front" and "behind" orientation properly.

 

Students began work.

Once they reached 12 pairs, they brought the ends around to join in a cylinder.

At this point, each pair of skewers is joined by one rubber band in the middle, and each interior skewer is joined to a neighbor exterior skewer by rubber bands at the top and bottom ends. To make room for more joins, the "end" rubber bands are slid in towards the middle. We'll then pair the ends to the new next neighboring skewer with a rubber band

This process is repeated until there are seven or more rubber bands holding each skewer to seven (or more) neighbors.

The constructed hyperboloid can be spread, or collapsed into a bundle of sticks.

Combinations are possible.

A good time was had by all (for the cost of a pack of skewers and a pack of rubber bands)

Hands-On Activity Workshop

As a Master Teaching Fellow at Math for America I have the privilege of participating in a variety of meaningful professional development opportunities. One such opportunity began this evening, with the first of a 3 session mini-course led by Dr. George Hart of Stonybrook University.

George first led us through a few drawing exercises -- draw a cube, draw a cube in an isometric projection style, draw a truncated cube, draw an icosahedron, draw a truncated icosahedron. At each step he gave us some pointers on key tricks to make our sketch a bit better. For example, judicious selection of the "front" can make the rest of the sketch so much easier.

In the background, we explored the relationship between vertices, faces, and edges. The point was not to derive Euler's formula, but it was a nice aside. (faces + vertices = edges +2) The real point though was to prepare us for a physical construction.

With our truncated icosahedron sketches as a guide, we took CD-R media and zip ties and began building a physical model of the icosahedron. CD with shiny side out represented the vertices, CD with dull side out represented the edges.

A good time was had by all.

Stuck in Tablet Mode

My desktop disappeared!

I've got a Lenovo Yoga ThinkPad, which I mostly use as a desktop, and sometimes use as a laptop, and rarely use as a tablet. I don't know if it's related to my Windows 10 upgrade, but last week after I flipped the computer open, it asked if I wanted to switch to tablet mode. Silly me, I clicked "yes."

The next day when I booted the machine, I had no desktop. Just the Windows 8 tiles. Ummm. Not what I wanted.

It took me a while, but I figured it out. It seems the default setting is, once you switch to Tablet Mode, that the machine will boot into whatever mode it was last in. I somehow was not doing whatever action triggers the sensor to know "get out of tablet mode" so it was just sitting like that. Other "features" of the mode are, you can't size windows -- they're either full screen, split screen, or minimized. Also, it seemed to randomly flash me back to the tile screen. Maybe that would be useful if I was actually using the machine as a tablet. Not sure.

Anyhow, here's the fix. From the Windows menu I went to Settings.
From Settings I went to System.
From System I went to Tablet Mode.
From Tablet Mode I was able to set the dropdown selection of "When I sign in ..." to say "Go to the desktop."

Problem solved. Took me a week.

Soft Circuits Workshop

Attended a workshop on July 29 titled To Code and Beyond: Soft Circuits. Workshop was led by Dr. Kylie Peppler of Indiana University.

It was a rushed four hours, but I'm excited to further explore the concepts and techniques I heard about. First off, soft circuits is related to physical computing. We worked with electronic and electrical components attached to textiles (felt and t-shirts) using conductive thread connect piece to piece. There is a lot more subtlety to the concept that can be covered in a short workshop, but we focused on LilyPad Arduino microprocessors.

So now I'm working on my first solo project.

I've attached the LilyPad to an old shirt. As you do this, you have to think about the "wiring" that will eventually connect other components sewn to the shirt. I've chose to put the ground (negative) terminal to the top, thinking I'll route all the positive connections low, and then have all the components share a bus back to the negative high.

I'm not sure how expensive conductive thread is (we got a couple bobbins of stainless steel thread on leaving the workshop) but, to save I've attached the LilyPad using normal polyester thread. Note I've used an embroidery hoop to hold my surface flat. I've attached at the negative terminal, and digital terminal 11. From here, I'll use conductive thread.

I'm also not sure what will happen with the battery. The Arduino needs power, but that lithium ion battery shouldn't be just dangling. On the other hand, I need to be able to detach it easily for washing, so I can't sew it firmly in place. Needs some thought.

Learning Ruby part III

Starting flow control.
If statements.
Behavior as expected. Note the comparison operator uses double equals ==. A single = is an assignment operator.
Note that elsif is not spelled correctly. That took me a while to realize why the code didn't work right.
unless checks for false value, opposite of if
exclamation as a prefix is like "not" -- != means "not equal"
&& conjunction
|| disjunction
How to use if, else, and elsif
How to use comparators / relational operators like ==, !=, <, <=, >, and >=
How to use boolean / logical operators like &&, ||, and !

String control with a daffy duckifyer. gsub

Check substrings .include?

Starting loops
while, until, for
no increment operator like ++ or --
instead, uses += with an delta value
range in 1...10 (exclude the end value) or in 1..10 (include end value)

loop method -- the iterator
break to exit a loop
next to skip an iteration
arrays to store multiple values
another iterator .each

Learning Ruby part II

Basic tutorial at code.org was just that -- basic.
Now I'm trying their next tutorial, which seems to deal with input and string manipulation.

gets accepts user input
gets inserts a blank line after the input. the method .chomp removes the line
gets.chomp accepts user input without adding an extra line

Learning Ruby part I

I have been given a task which requires I learn Ruby. I will try.

I've installed Ruby on my laptop (from links at ruby-lang.org). I found a tutorial on code academy. So I'll see where this leads.

notes:
data types: number, boolean, and string
assignment operator: equal sign
exponentiation: **
modulo: %
print: sends to screen
puts: adds blank line after screen output. hmmm?
I see. print leaves the next output right there, puts goes to the beginning of the next line.

strings have .length
and .reverse
and .upcase and .downcase

hashmark for single line comments
=begin to =end for multi-line comments

Why I'm Uneasy With Nerds On TV

I am a nerd. I scored very well on SAT, GRE, GMAT, and Praxis tests, and generally can perform well on standardized measures. I enjoy working mathematical puzzles. I think precision and accuracy in language is important.

But as far as I know, I am nowhere on the autism spectrum. I have many normal social interactions. My speaking voice is neither whiny nor squeaky.

I do not use suspenders to hold my pants with the waistline above my navel. Nor is my inseam so short as to reveal my socks when I stand. I wear eyeglasses neither held together with tape nor featuring lens diameter outsized for my face proportions.

As a math teacher, I hear many colleagues speak glowingly of TV shows which have a "nerd" as leading character. They say they like to see smart people cast in a positive light. They assume these shows are my favorites.

But I am uncomfortable with what I've seen of these shows. I find the caricature of "smart" people demeaning. I dislike the implication in the writing that "smart" is an innate quality and cannot be developed. I question the choice to cast smart people, with possible exception of the lead, as physically unattractive.

My school holds a Spirit Week each year for seniors, where each day is devoted to some theme. Last year's Spirit Week included a Nerd Day. Most of my seniors came to school dressed in some ridiculous stereotype portrayal of "smart person." I wrote to my principal and suggested that, perhaps, this was not the correct message to send to our students -- that being able to perform academically makes one a target of ridicule. I think we should celebrate our students who achieve, not hold them up for derision.