Research days - magnetic building sticks

At the end of September every year Norway celebrate scientific research with a slew of national events. Here in Trondheim we have two days of a 'Research Fair' where folks from education and industry set up stands inside two huge tents in the middle of downtown. Friday we welcome schools and Saturday we're open for the public. This year's theme was "Society". The Math Center (my workplace) teams up with the Math Institute every year, and this year our team met several times to create building materials so kids could make polyhedra and learn about how polyhedra contribute to art, arcitecture and science.

We glued magnetic balls to the ends of 50 cm long sticks, and they worked remarkably well as building materials. We decorated our stand with posters showing polyhedra in art, architecture, science and everyday living, and we also constructed a newspaper geodesic dome that we placed on top of our stand (see earlier post for instructions). We had three tables and a carpeted area for building. For two days we built stuff with kids and it was fantastic fun.

 

We found three different designs for towers. Height was limited by the strength of the magnets, but we were able to build two of the designs to heights over 2 meters. Amongst the Archimedian solids we built: tetrahedra, octahedra, icosahedra, and a truncated tetrahedra (I thought it would be impossible, but we did it), as well as several cube variants though they required different structural supports because of the unstable nature of squares.

Here's some pics of the construction process. We bought flowers sticks from a craft shop and Bucky Balls, strong magnetic balls that are awesome to play with by themselves. With a glue gun, put a small dab on the end of a stick, press a ball into it, and after it has cooled place a small amount of glue on the seam and then rotate the stick while smearing the glue around the seam with the tip of the glue gun. The glue should reach up the the midpoint of the sphere or a little higher. If done properly (it takes practice!) there is only a small amount of glue but the magnet is fastened strongly to the stick.

To be determined by further research: is it better to have the poles parallel or perpendicular to the stick? My feeling is that perpendicular will make for a better building experience. The first picture below shows the magnet being attached parallel to the stick. This gives less opportunities for sticking to other magnets, though the attraction will be stronger when it does align. I am unlikely to build another set so I may not know, but should you wish to make a set, you might want to try both and let us know!

Bridges Gallery 2012

Three of my works were in the Bridges Gallery this year in Towson, MD.

Binar, an image based on the binary numbers from 0-127 (0000000-1111111)

Pentamen Spiral

The Human Cube

Math Munch

I met a lot of great people at the Bridges conference this year, among them Justin Lanier, Paul Salomon and Anna Weltman, authors of the Math Munch blog. They did a short write up on my stuff that you can find here: http://mathmunch.wordpress.com/2012/08/06/mike-naylor-math-magic-and-mazes/

Be sure to check out the other stuff they have on their site. Good stuff!

The Human Kaleidoscope

Here's my film that debuted at the Bridges International Math Art Conference in Baltimore, MD, July 2012.

Ballooning with Vi Hart

Vi Hart ran a mathematical balloon sculpting workshop at the Bridges conference in Pécs Hungary summer 2010. Here's the effervescent Vi with an icosahedral balloon sculpture, and me inside her group project Sierpinski pyramid. Squeaky fun!

Pi acknowledgement

In Sandra Kring's novel "Thank You for All Things" (amazon.com link), one of the characters is an autistic child who memorizes pi and is close to the world record. Here's an excerpt about one of his practice sessions:

As I pass Milo’s door—eight hours after he began—he’s resetting his timer.  He sees me and calls out, “I’m just starting position 48,551,” he says.  “I’m averaging 6000 digits per hour.  Right up there with the current record holders,” He sets the timer down and starts, “three, seven, two, five, four—I really like that part!—eight, two, five….”  The sounds of Grandpa Sam’s rutted breaths and rattling bed bars are filling every corner of the house.  Milo hears them too, of course, and I can tell by his eyes that he’s grappling hard to see the digits, rather than to see Grandpa struggling to breathe.  I feel sorry for him, so I say, “Good job. Catch you later.”  

 The part he likes, 3 7 2 5 4, is my name in sound numerals. A cool 'secret reference'.

Find out more about sound numerals here: http://folk.ntnu.no/krill/home.htm

Human Hypercube

Speaking of hypercubes, here's representation with people. We can build up to a hypercube by starting with a 0-dimensional point. 'Stretching' that in one direction gives us a 1-dimensional line segment. Stretch the line segment in a direction at 90° from the line segment and we get a 2-dimensional square. Stretching that 90° from the plane of the square gives us a 3-dimensional cubes. Now, stretch the cube at 90° from its volume (yes, I know it hurts to try to think like that. It's only impossible in the real-world, not in your mind!) and you'll have a 4-dimensional hypercube.

The pictures above show the changes from 0-d to 4-d.

Puzzles:
1. Describe how the number of vertices changes. Write a formula.
2. Describe how the number of line segments changes from one figure to the next. Write a formula.
3. Describe how the number of squares changes. Yep, formula.
4. Describe how the number of cubes changes.
5. Predict the properties of a 5-d hypercube. Can you draw one?