While on vacation, I passed some of my time looking for math on the beach, and I saw a sine wave creeping up the shore.
I thought I might be looking too hard for something mathematical, thereby seeing things that weren’t really there. Thankfully, Geogebra is well-equipped to justify my observations.
Or perhaps it’s more accurate to say that Geogebra helps enable my obsessions.
W
hen it comes out that I’m a math person, the most common response from people I meet is “I was never very good at math“. After a lifetime of struggling to find the appropriate response, I finally have something positive and proactive to say: go get yourself some electroshock therapy.
According to a recent study, running a mild electric current through the brain seems to temporarily increase mathematical ability. Apparently the study involved teaching the subjects a new numeration system (could it have been octomatics?) and testing their ability to organize those symbols before and after electrical stimulation of the parietal lobe.
In addition to slightly increasing mathematical ability and potentially treating dyscalculia, there is hope that such electrical stimulation could improve other brain function, as well.
Now, how can I bring this revolutionary technique into my classroom?
This graph on the right represents break ups per day, as determined by an analysis of Facebook status changes. The data suggests that break-ups seem to occur most frequently in mid-February and late November.
Drawing conclusions from data is always dicey, and there are probably a lot of holes to poke in the methodology here, but it certainly is fun trying to attach meaning to these numbers!
This graph was featured in a TED Talk given by David McCandless, who runs the wonderful website www.informationisbeautiful.net.
The whole talk can be found here; this chart comes up at around the 6:50 mark.
The amount of data available through social networking sites is mindblowing, and it can’t be long before it will be used in some significant way. Indeed, a group of MIT students has already devised a system, cleverly titled Project Gaydar, that, with some accuracy, identifies the sexual orientation of a Facebook user based on friends, likes, and other connections.
What will they compute about us next?
In general, it’s unusual for a rectangle to have sides and diagonals whose lengths are all integers (i.e., whole numbers). Consider the following three rectangles, all of width 3:
Looking at the different lengths, we see one place where the diagonal length is an integer, but in the other cases, the diagonal length happens to be a non-terminating, non-repeating decimal (i.e., irrational). Indeed, the diagonal length will be an integer exactly when the length and width are part of a Pythagorean triple, but compared to the alternative, this is uncommon. (While there are infinitely many occurrences of this, we can still meaningfully consider it uncommon).
Now, imagine the situation in three dimensions. A rectangular prism (think of a cardboard box) has 12 sides, 12 face diagonals, and four space diagonals. It would be extremely unusual for all of those 28 lengths to be integers. Even if we didn’t limit ourselves to rectangular prisms, but we allowed for the box to be slanted in all directions (that is, a parallelepiped), it would still be a numerical miracle for all those lengths to be integers.
Well, meet the perfect parallelepiped!
This was discovered by a couple of mathematicians at Lafayette College in Pennsylvania, using brute-force computer trials. It looks like they found some others, too. So thank you, Clifford Reiter and Jorge Sawyer, for giving me an extra credit problem for my next exam!
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This is a thoughtful and hilarious satire of old-school, British public television-style educational videos.
http://www.youtube.com/watch?v=Pj2NOTanzWI
I laughed repeatedly throughout. Watch the video, and give it a minute or so to win to you over. It’s worth it.
P.S. Students–please do not bring razor blades, Garry Gum, or Anti-Garry Gum to class in your pencil case.
Thanks to Ivan R. for showing me this!