Coloring Theorems

Yesterday I gave a talk for middle school students at the GMU Math Circle showing that all the countries of the world (or any other round world) can be colored with only four colors (the rule being that no neighboring countries can be the same color.)

Actually, I didn't prove the four color theorem, because as  of yet, nobody has proved the whole thing without computer assistance. 

However I did prove (using only middle school math mind you) that the number of colors needed to color any flat map is not more than five. 

Amazingly, the answer is completely different on Planet Dunkin

on which maps can require at most SEVEN colors. and to illustrate this, I printed out this model of the torus with seven countries, all of which touch each other. 

Torus model  http://www.thingiverse.com/thing:721430 by BonyJordan. (Scaled up for classroom use. Original is half this size.)

Note this map coloring problem has an interesting history,  which I include from my talk (adapted for web attention span,  meaning I removed 90% of it):

Scanning with an iPhone

I tried out   the iPhone app 123D Catch for 3D scanning. You take many photos of an object from different angles. It uses the phone's accelerometer to know which relative angle you are located at. Here is the scanned image of a banana.

After a fair amount of cleanup of the data in Meshlab,  here is the corresponding 3D printed banana. 

Not as tasty as the original, but regardless a very impressive job. Unfortunately, my experiments with human heads are so far not nearly as successful. (I have yet to scan one that's printable.) 

Frog Innards

Here's a way to practice before the actual dissection. Practical? I don't know. Seems like it might help to learn the parts prior to having to take them out.

STEM Camp Poster

As a follow up to the STEM camp for middle school girls, each group of five campers was assigned an  to create a poster about one of the STEM activities in their camp week. They then had to give a formal presentation of their poster to the parents. Here's the poster on 3D printing:

FOCUS STEM Camp

Yesterday was the STEM camp for middle school girls. Everyone seemed to enjoy learning about 3D printing and designing their own print.

Here they are hard at work:

The final products of 16 groups of 5 campers each. The resulting tiles will be made into a mosaic. 

GMU STEM Camp

Working on an activity for a GMU STEM camp for middle school girls next week. This activity is designed to take an hour. The result is a tile. The plan is for each group to make a tile, and the set of tiles will form a camp mosaic. Here are the samples with a penny for scale.

Here are the instructions. (I believe you can view this to see it full size if it isn't readable inline.)

Looking forward to seeing what the campers come up with. 

Odyssey of the Mind Trophies

Personalized trophies for the seven members of the Odyssey of the Mind team I coached with Jeff Offutt. Each side is a wordle of lines from the scripts. The print consists of five pieces (four sides and a middle) attached with ABS slurry. Largest production item I've ever made.