Mathematics and Castles: A Perfect Day!

Wednesday was terrific. In the morning we went to Bolyai Janós Gymnasium, the school hosting us, and visited a double-period math class on the equations of a circle in the plane. After a slow start reviewing equations of lines (using parallel vectors, normal vectors, slope-intercept and point-slope forms), the teacher introduced the equation of the circle and asked a series of questions about equations of circles, involving progressively more geometry and more involved algebra. Towards the end of the first half, she posed a tangent line problem and called on our students to help solve it; Jerry suggested using calculus (much tsk-tsking from all three math teachers) and presented his solution, but Sam and Vlad had geometric solutions that were quite nice. After the break, the teacher posed the problem I posted earlier, and had a Hungarian student start it using geometry. But as the calculations grew more involved, the teacher suggested that maybe another approach would be better. Alex came to the rescue [students, where are your pictures?] and gave a really elegant algebraic derivation; Mr. O'Roark and I then offered two geometrical solutions. Our students had fun participating, and even though the teacher didn't get through all the problems she had planned on solving that day, I think it was exciting to get stuck and then unstuck, and to see so many ways of solving a single problem.


Then we had a walking tour of downtown Salgótarján; although it was cold and drizzly, we made the best of it. I made my first successful purchase in Hungary: three Umbrellas (690 Ft, about $4 each). I gave two to Alex and Jerry (they had forgotten theirs in Chicago), and kept one for myself. (Left, Jerry standing on one of the stones demarcating the border between Hungary and Slovakia--notice the camel motif.) The tour included lots of history of the communist and post-communist era in Salgótarján, which was interesting "recent history" for many of our students.

After lunch at Bolyai, we visited the mayor (students, more pictures?) and trekked to a nearby castle--a trip that the rain had made our hosts suggest we scrap. But the weather, and the mud, didn't dampen our spirits at all: we hiked up the hill to the castle, around the ruins, and down to a nearby geological formation.



The castle was beautiful in the mist, and even though it was drizzling all the way up, everyone stayed in good spirits.





At right you can see us having fun with the arrow slits and "murder holes," through which castle defenders would pour boiling oil on invaders.


After all that, the parents threw us a party in a local disco, culminating in a huge cake with sparklers: