Overlapping circles on the kit.
Appreciation
Clark Kent is a Superhero
It was superhero day at school, and a senior had donned some fake glasses as his costume. Confused, I inquired as to which superhero he was supposed to be. “Clark Kent,” he said. “Clark Kent is not a superhero,” I said. “Superman is a superhero, and Clark Kent is his alter ego.”
A rousing debate ensued. Well, it wasn’t really a debate; it was pretty much me against everyone else.
“No one calls out for Clark Kent in desperation,” I said. I was being difficult in my typical way. Yes, I was trying to make a legitimate philosophical point, but mostly I was just trying to intellectually irritate the students. The controlled chaos of classroom debate continued
“Bruce Wayne is not a superhero!” I was growing more confident in my stance, and sensed the argument drawing to a close. I was ready to claim victory. Then a clever student raised her hand. The class quieted.
“Clark Kent is Superman. Superman is a superhero. Therefore, by transitivity, Clark Kent is a superhero.”
In a rare moment, I had no clever response. In light of this stunningly elegant argument, I was forced to concede. But I’ll be back.
Challenge Geometry
Fun With One Cut
Inspired by a brilliant talk by Erik Demaine, I started playing around with the famous one-cut problem: given a shape made up of straight line segments, can you fold the paper flat in such a way that with only one straight cut your shape will appear?
Having no real experience with mathematical paper folding, I thought I’d try out a Koch Curve. Well, a finite iteration of it, at least.
It seemed like the strategy was to use the symmetry of the shape to make all the line segments line up on each other. So I folded down the middle, and then again down the new middle.
I rotated the last shape and it seemed a little clearer how to continue.
It seemed like all the lines were lined up, so to speak. So I cut. And voila!
Not too bad! Now, if I could just figure out how to do this with non-symmetric figures.
Related Posts
Challenge Game Theory Technology
Rock, Paper, Scissors
This is a great interactive Rock-Paper-Scissors game from the New York Times website:
http://www.nytimes.com/interactive/science/rock-paper-scissors.html
The computer will narrate its strategy for you as you play, telling you whether it has correctly predicted your choice or not.
Skeptical? Play the game against the Veteran computer and watch it beat you! Then, go check out this infographic for some tips on how to improve your play.
It might be fun to pit a 6-sided die against the computer to see what happens.
Technology
Another Mechanical Calculator
This video demonstrates the Original Odhner mechanical calculator.
http://www.youtube.com/watch?v=Bz8_tNDUDog
It looks like a miniature typewriter, and it seems to operate in the same manner as the Curta mechanical calculator: switches allow you to “input” numbers into the machine, and then turning a crank performs addition or subtraction.
The video demonstrates some basic operations of the Odhner, and it includes a nice (if lengthy) computation of the square root of 2 that involves a few arithmetic tricks.