Tuesday, March 25, 2014

Printing 25 March 2014 (and Egg Holder POC)

After another lesson with George Hart at the MfA offices, I was pumped to try out what I learned.  So I took the printer up to after-school tutoring today, to slice and print in the background while I worked with students. I expected my egg holder would take time to calculate in Mathematica (large number of PlotPoints), so while that was running in the background I decided to fill out my collection of Platonic solids. I downloaded a hexahedron (a.k.a. "cube") that's a Hart design which somebody uploaded to thingiverse. Note the link is to a collection of items, of which the cube is a member.

Printing the cube was uneventful until the top cross-edges. I was intrigued to note that the PLA bridged the uprights perfectly in the front-back direction, but drooped in the left-right direction. At first I was dismayed, but then I realized it looked interesting, and let the job continue. After a few layers the software shifted direction, and laid down enough support that the drooping spaghetti effect stopped. I'm interested that this happened in one direction only, and, since the faces of a cube should be congruent, wonder why it happened.

Although the photos below show the thing on my print platform, it's after I've lifted it from the plate, and rotated to try to get a good photo. (Canon PowerShot SD970 IS in macro focus mode)

Although my egg holder finished plotting earlier, the cube took over 50 minutes to print, so I didn't have a lot of time left for that. Basically, the function was a sum of sine curves in the x and y directions. Function call was
RegionPlot3D[ Abs[z - (Sin[2*x] + Sin[2*y])] < .1, {x, -3*Pi, 3*Pi}, {y, -3*Pi,   3*Pi}, {z, -3, 3}]
There were a lot of holes in my surface, so I had to step up PlotPoints. Each tick up increases the calculation time for the RegionPlot, but at each increase there were still holes. It wasn't until I got to PlotPoints->300 that the surface looked smooth and continuous. But took forever to calculate.

Time was short, so I decided to try printing as the .stl from Mathematica loaded in MakerWare, which is tiny because of the scaling issues with the .stl format. But, as I was warned, doubling the size would roughly octuple the print time, since it would multiply the volume of plastic used eight-fold.

Print was obviously failing from the start. It wasn't sticking to the print platform. So I cancelled the job, and tried again with a raft. This print was successful, even if ridiculously tiny. But it serves as a proof of concept. That is, my sinusoidal egg holder is a viable design. When I have time, I'll try the printout again at double size. Since this tiny one took just over ten minutes, a double size should take under an hour and a half.

Friday, March 21, 2014

3D Printing Friday March 21

This would be much more convenient if I had a secure place to leave my printer. But I have to lock it in a cabinet, and I really only can work with it after school. So today I decided to stay late and try to print.

One issue last time was the thing didn't stick to the print plate. I've found this comes from two causes. To remedy one, I covered the print plate with blue painter tape. This will also help release the finished thing from the print plate, which has been a problem in the past.

I tried printing again, and as the MakerWare software was slicing my thing (the egg holder) I realized another problem. I have edges floating in space. Duh! Of course that won't print well. I need to design a frame around the thing, or else print with supports.

Once the print started, even before it got to the point of hanging objects, I could tell the print wasn't going well. The print still wasn't sticking to the plate. The way it was coming loose, I think, is associated with the plate being out of level. So I canceled the print job in order to level.

As easy as it is in theory to level the plate, it isn't a precise science. The instructions say "raise the plate until you feel just a little friction between the print head and the plate." There's a lot of room for interpretation in that instruction. So I decided to try something that I know I've had success with in the past, and keep trying until it came out good again. That was the five link chain that comes preloaded on the SD card with the printer. After three tries, it printed perfectly.

By this time, it was already 4:30, and I was tired. I wanted at least one nice thing, and didn't want to experiment with my own bad design again. I went to thingiverse and did a search under "hart" to see if I could find any George Hart designs. Sure enough, there are a few available. I selected an open dodecahedron sculpture, downloaded, and sent to the printer. It took almost an hour, but I did end the day with a lovely dodecahedron to show for my efforts (even if it wasn't my own design).

I'll work more on my egg holder this weekend, and, if I have time, try to print during the day Monday.

Wednesday, March 19, 2014

Group Work as the Norm

This semester I am very fortunate to be working with a fantastic Student Teacher. He, also, is with MfA, and he had a full semester with another Cooperating Teacher at  different school. He came to me already well at ease in the classroom, with good management skills.

As an MfA member, he goes to workshops periodically, and last week attended one on group work. He asked if he could try some of the techniques in our class. I said sure. Today was the trial.

Before students arrived, desks were arranged in groupings of four, with a group number posted on one of each grouping of desks. Five rules were written on the board.
1) You must make sure each member of your group understands the instructions.
2) Each group member is responsible for answering all questions fully
3) If members of the group disagree on an answer, they must discuss until they come up with a single answer for the group. All group members must be able to explain the group answer.
4) Before you may ask a teacher a question you must ask each of the members of your group to answer the question.
5) You may not talk to members of any other group.

We had a worksheet with a few questions comparing volume and price of donuts versus donut holes, and asked for surface area of a cake with the same volume as a dozen donuts.

I have never seen my students so engaged.  All three geometry classes had better than 95% of students actively involved in discussion, sense-making, hypothesis testing, and doing mathematics.

The person who led the workshop apparently says he exclusively does group work. I'm not sure how that works out, as I think there's some material that requires at least a bit of teacher presentation. But I certainly see how this technique could be very effective in my classroom on a frequent basis. I look forward to exploring more with it. The difficulty seems to be in coming up with group projects day after day.

Today was a positive.

Tuesday, March 18, 2014

3D Printing part 5

I finally received my new laptop, so I was finally able to install Mathematica with full license. This means I'm able to export to .stl format, which is needed to communicate with MakerWare.

One of the homework assignments from class was to make an "egg carton." I decided to start with an egg holder without lid. Not really a carton, but I figure that's fair since I'm a beginner.

Although I tweaked the parameters a bit, basically my surface is z=sin(x)+sin(y). Mathematica draws it with lots of gaps, so I needed to increase PlotPoints up to 200 before it looked even close to okay. That significantly slowed down the plotting.

Once I had a plot, I exported to .stl. The syntax of the command is Export["filename",whattoexport], which took me a while to figure out, because I was too lazy to look up the help reference. In the end, I would have saved time by looking it up first.

Next I opened the file in MakerWare, which immediately asked permission to put the drawing on the platform.  Good call, I thought. It looked really tiny, so I tried scaling it up, and clicked the command to print.

The Replicator 2 makes all sorts of cute noises as it prints. I let it run for a while, but it became clear I wasn't getting good results, I think I need to level the Plexiglas surface. Try again tomorrow.

Monday, March 17, 2014

Arduino Day 2

Second Arduino workshop. It was a whirlwind, and hard to keep up just typing code.

Learned about Pulse Width Modulation to a digital pin. Wrote a program to fade in and out.
Then worked with a speaker, making noises, which gets old very quickly.

Good fun. I need to redo some of these things on my own, to make sure I really get them.

Friday, March 14, 2014


Some time ago I happened upon instructions for a Mathematically Correct Breakfast which involves slicing a bagel in such a way that it forms two linked rings. I practiced the technique, and have since amused myself by showing off whenever given the opportunity.

Fast forward to last Monday when I had my first class in 3D printing with Mathematica and Makerbot Replicator 2. The teacher is George Hart. George Hart is the man who wrote the instructions for the Mathematically Correct Breakfast.

Next stop, this morning, as I followed an acquaintance's Twitter link to a video called Anti-Pi Rant. The video was created by mathemusician, Vi Hart. But wait. Can it be? Vi Hart is George Hart's daughter?

I need to take a break to eat a hexaflexa-burrito.

Tuesday, March 11, 2014

Arguing Angles

I'm working with a group of other Geometry teachers in my school trying to plan lessons together. Monday afternoon we got into a heated discussion. The topic? How to define the major arc of a circle.

We all agreed on the textbook definition of a minor arc: if the measure of the corresponding central angle is less than 180 degrees, then it is a minor arc. But the dispute was about the definition for a major arc.

My colleagues wanted to use parallel language, saying it is the arc for a central angle greater than 180 degrees. But our text has never discussed what it might mean to be greater than 180 degrees. In fact, were we to allow angle measures greater than 180 degrees, then we lose the definitions of "interior" and "exterior" of angles, and consequently a multitude other relationships become ambiguous or wrong.

I'd rather go with our textbook's definition of major arc, which uses the idea of "not interior to the central angle." This maintains the idea of angle being less than (or equal to) 180 degrees, and preserves definitions of  interior. But my colleagues say this is too complicated, and our students can't handle it.

My colleagues argued that in Trigonometry we regularly use angles much greater than 180 degrees and much less than 0. But I pointed out that in Trigonometry, in order to go beyond 90 degrees, we must view angles as rotations, while in Geometry they are static. This didn't persuade them.

We regularly have discussions about rigor, and holding our students to high expectations. How can we on one hand water down content and on the other hand say we are rigorously holding high expectations?

Monday, March 10, 2014

Mathematica and Makerware and Replicator 2

Today was the first Math for America mini-course session on 3D Printing, led by George Hart of Stony Brook University. Mostly what I learned is how amazingly easy it is to use Mathematica as a design tool. Essentially, you plot whatever 3D function it is you're working on (RegionPlot3D), and export that plot to an .stl file. Done.

Currently, the biggest issue is that I'm using a trial version of Mathematica, which doesn't allow export. But my new laptop is supposed to arrive in a few days, and I'll install the full version of Mathematica on that. Then I'll be good to go.

My homework: design and print a knob for a rotary light dimmer switch, and design and print a carton for (an unspecified number of) eggs.

Tuesday, March 4, 2014

T^3 International Conference

Heading off for the annual conference. This is always a nice event for me as a teacher. On Thursday I conference with other TI Instructors. On Friday and Saturday I get to meet with other math and science teachers from around the world to share practices. Should be a good event.
(I expect my twitter activity will increase dramatically for the next few days).