Sunday, November 25, 2007

Trondheim Math Trail

Today we kicked off the math conference with a Math Trail around Trondheim. I was very worried this morning as the snow was falling in clumps, and I did not bring a pair of boots (too much stuff to bring to pack boots!) But the sidewalks were passable and it was warm despite the snowfall.

In groups of 10 we explored the city, solving math problems along the way. Here I am on the footbridge in town with the moon low in the sky.

This sculpture was fascinating: it is based on a magic square. It took me a while to figure out the magic-squareness of it. The secret lies in the heights of the posts. In each of the four corners are 9 posts. The center posts of each set of nine are all the same height -- these are the 5s. They are connected by a blue square in the middle of the tangle of metal above (which you can see better in the first picture below). The other posts are of heights to represent the other digits 1-9, and they are arranged in a 3x3 magic square layout in each corner. I will return to study this in depth... is the magic square different in each corner? Are there only 4 unique solutions to a 3x3 magic square (discounting rotations and reflections)? And is there a pattern or meaning to the way the numbers are connected between squares?

This evening, Pam and I joined conference-goers for a banquet at Grenaderen, a hall on the river near NTNU. We sat with a group of teachers from Bergen, and after some initial awkwardness (we were strangers in a group of friends and did not speak Norwegian), we ended up having a great time and scoring invitations to visit Bergen and come see their school. A very nice day indeed!

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