Jason Dyer Isn’t Human

Pity the poor bloggers who don’t have Jason Dyer running wild in their comments. He’s holding court right now in my last post, running something like a mathematical Total Request Live.

People drop by and say, “Hey, does anyone have an engaging, concise problem to motivate (eg.) matrix row reduction?” and Jason pops back with an awesome seven-word problem involving \$5,000,000 in a stolen leather satchel which covers the entire standard.

You’re like, “Cool, but can I see that in a tenth grade,” and the dude obliges.

Credit, also, to Steve Peters, my UCD roommate, now at MIT for a doctorate in robot clouds or something, for putting his big brain to use around here.

What I’m saying is that perhaps I have underestimated these internets of yours, thank you.

I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. He / him. More here.

1. Jason Dyer

May 8, 2008 - 2:51 pm -

There ought to be an arbitrage problem hiding in there. (Arbitrage is where you make money simply by shifting money around to different currencies to exploit the fact that because of minute variations going from \$1 -> peso -> euro -> kroner -> dollar might not get you \$1 back, but more like \$1.00004. You need a _lot_ of money to pull off a profit though. More like \$50,000,000 than \$5,000,000 anyway.)

I’ll have to give it some thought, though.

2. Jason Dyer

May 8, 2008 - 3:29 pm -

Okay, here goes:

How can we make money by converting currency?

(Eight words, not seven. Sorry!)

Basically if you take a matrix of currency conversions
———–Euro—- Peso —- Dollar
Euro 1 2 4
Peso .5 1 2
Dollar .25 .5 1

(Read: for every 1 Euro you can get 2 Pesos, or 4 Dollars. For every dollar you can get .25 Euro or .5 Pesos. I know, not accurate, just an example.)

and you do Gaussian row reduction, and everything is balanced properly, you’ll get this
———–Euro—- Peso —- Dollar
Euro 1 2 4
Peso 0 0 0
Dollar 0 0 0

but if there’s an imbalance that can be exploited via arbitrage, you’ll get something more like
———–Euro—- Peso —- Dollar
Euro 1 2 3
Peso 0 0 .25
Dollar 0 0 1

Of course in real life this happens at a much faster pace with more sophisticated mathematics and generally you have to take a “path” through currencies to make anything, but this get off the basic idea.

3. Benjamin Baxter

May 8, 2008 - 6:22 pm -

I need lessons that cover the geometry standards, with an emphasis on the first half.

4. Steven Peters

May 9, 2008 - 5:24 am -

Wow, mad props Jason. The only row reduction examples I can think of right now are related to circuits or trusses. Finance may be a bit more interesting to the average student.

Dan, thanks for the props. I get to do interesting research at school, but I’m not doing any teaching right now. This is a fun community to interact with, vicariously if need be.

5. Kate

May 9, 2008 - 6:02 pm -

Srsly….solar hot dog cooker? *bows* (in a “we’re not worthy” fashion)

6. Jason Dyer

May 10, 2008 - 7:26 am -

I don’t have time for a full write ups on these, but both the questions would make a semester-ender that would include chapters one-six of the Discovering Geometry book (vocabulary, patterns and proof, construction, triangles, polygons, circles).

How could we figure out the value of pi by hand?

[I’m thinking the Archimedes solution, with inscribed polygons. Difficult to find and requires all the resources the students have (including construction!), but it doesn’t use anything past the first half of geometry.]

What’s the center of gravity of the wings on this aircraft?

http://en.wikipedia.org/wiki/F-102_Delta_Dagger

[Presuming flat and equal weight distribution for simplicity here. Any aircraft with triangular wings will do. Basically you are trying to get the students to discover the centroid on their own, which is one of the trickiest constructions. The neat thing here is they can set up experiments with pieces of cardboard to find centers of gravity on other triangles and make hypotheses.]