Today was that funnest day of the semester in MATH 280, when everyone gets to take a trip back to the third grade as we play with L-tiles in order to understand the idea of induction. This day is always a fun one, but I don't think any 280 class has ever had as much fun as these folks did. They loved it!
Friday, February 11, 2011
Fun with L-tiles
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Do tell a little bit about what you are doing with the L-tiles? Please?
They're L-shaped tiles with short sides of length 1 and long sides of length 2. This "unit" tile we call L1. The tile Lk is the shape formed by scaling this one by a factor k.
You can prove through a three-case inductive argument that one can build Lk out of non-overlapping Ls, for any positive integer k. We were constructing an intuitive skeleton for that argument.
We all had so much fun with this project! Such an interesting way to begin learning about one of the harder methods of mathematical proofs!
Please don't tell me this is the only fun day we will have all semester. We have another 2.5 months!
@Anonymous: are you saying class isn't typically fun? I ask this somewhat seriously: though the primary goal of the class is not to have fun, having fun while learning certainly helps, and if there's anything I can do to make it a more relaxed and pleasant atmosphere, I hope you know that I will. Suggestions?
Only fun day? Math 280 is loads of fun! We get to watch Patrick kick over calc books to teach us proof by induction. Not to mention we got to use L tiles as a visual learning tool and introduction to the proof style. In fact, I feel that the way that Patrick teaches mathematical proof adds an extra layer of flavor and color to the subject that may otherwise seem dry and slightly lethargic. DON'T CHANGE ANYTHING! Maybe more mass chanting when we arrive at a contradiction, but other than that DON'T CHANGE ANYTHING!
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