Myself and my partner recently jetted off for a week’s holiday in Bolivia. We arrived by air into La Paz, spent the first night in the hotel to acclimatize to the high altitude and then set off for the famous Salt Flats in Uyuni.
After a treacherous 11 hour bus journey, in which a person actually dislocated their shoulder through an extreme six-hour period of bumps, we fortunately arrived in Uyuni in one piece. Even though I was ridiculously fatigued, I couldn’t help but notice the hexagonal tessellating road pattern as I got off the bus. I didn’t even bother asking my fiancée if she’d ever seen this type of road pattern before because she was in desperate need of a shower and sleep and since her energy levels are directly proportional to her ability to look interested in my constant mathematical dribble, I simply decided to take a picture of the road and left it at that.
The next day, we hopped on a jeep to see the salt flats. Ignoring for now the fact that it was one of the most amazing places I’ve been to in South America, I couldn’t help but be surprised by the hexagonal tessellation pattern on the flats! I immediately wondered whether the Bolivians got the idea to pave their roads with hexagons from the naturally arising hexagons on the salt flats. Unfortunately I couldn’t find an answer to that question and I still don’t know why the salt forms hexagonal structures on the flats. (If anyone can shed light on this I’d be interested to know the science behind it).
Anyway, I thought that it would make for an interesting start to a tessellation investigation with my year 8’s and set them off on the task for 3 lessons. These are the questions I posed:
1) Which other shapes would work well for paving a road? Which shapes wouldn´t work well?
2) What´s the mathematical reason why some shapes fit perfectly together and others don´t?
3) Is it possible to use two or more different shapes to pave a road?
They wrote reports using geogebra as an aid and we discussed the best bits of each report. I wondered after if I should have shown them some Escher style tessellations to really get their imaginations flowing?