Through Math for America, I am part of an on-going collaboration with the New York Times Learning Network. My latest contribution, a Test Yourself quiz-question, can be found here:
https://learning.blogs.nytimes.com/2012/05/14/test-yourself-math-may-14-2012/
This question is based on the complex methods companies like Apple use to reduce their tax bills. How much more would Apple have to pay if it were taxed like an individual?
In honor of today’s date, 5/13/12, I honor one of my favorite triangles: the 5-12-13 triangle.
Of course, one reason this is a such a nice triangle is because it is a right. We can easily see that the side lengths satisfy the Pythagorean Theorem
Another reason I like this triangle so much is because it plays a part in another of my favorite triangles: the 13-14-15 triangle!
What a cool idea: a free software package that simulates a planetarium on your PC!
Preloaded with 600,000 stars, all you have to do is set your coordinates and start gazing!
You can search by name for various heavenly bodies, map the constellations, and even get close-ups of observable planets!
I’m not sure if this technically qualifies as a harmonograph, but the images produced by this cool apparatus definitely remind me of Lissajous curves.
The video of this device in action, from Robert Howsare, is definitely worth a look.
An interesting challenge would be to come up with the parametric equations of these curves based on the angular velocity of the two turntables, much like what can be done with actual harmonographs.
This is an interesting article by Jonah Lehrer of the Wall Street Journal about the limits of standardized testing.
https://www.wsj.com/articles/SB10001424052748704471904576230931647955902
Lehrer discusses the results of a study from the 1980s in which psychologist Paul Sackett attempted to measure the speed of supermarket cashiers. A short “check-out test” was developed which involved scanning a small number of items. The test was administered, and resulted in a list of the fastest cashiers.
What is interesting is that when Sackett compared the results of the test with long-term data collected by the electronic scanning systems, there was a surprisingly weak correlation between the results of the speed test with the data from regular usage. That is to say, there was no real connection between being fast on the test and being a fast on a day-to-day basis.
Sackett’s misconception, and perhaps one held by many, is that there is a natural correlation between maximum performance (that on a short test) and typical performance (that is, under normal, day-to-day circumstances). Tests like the SAT, the GRE, and other high stakes tests, are tests of maximum performance. Our educational system relies on these more and more, but are we sure they measure what we assume they measure?
Lehrer points out that individual success is determined more by character traits like perseverance and self-control, but of course, it’s hard to capture that in a timed, multiple choice exam.
