I was making lemonade the other day, and this happened.
which of course, equals, the following:
There you have it: the sum of the first three triangle numbers is the third tetrahedral number! Proof by lemons.
Economics Statistics
Yet Another Way to Lie With Statistics
This is a nice takedown of some spurious economic analysis, courtesy of Freakonomics:
http://www.freakonomics.com/2011/03/30/how-to-spot-advocacy-science-john-taylor-edition/
Looking at the graph at the right, it’s hard not notice the negative correlation between the two given variables, and the economist in question uses that correlation to bolster his policy argument.
The graph looks a lot different, however, when you look at all the available data, not just the data between today and the arbitrarily chosen cut-off of 1990. But that chart doesn’t support the argument as decisively.
As the author suggests, “Be wary of economists wielding short samples.”
Challenge NYT
Math Quiz: NYT Learning Network
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/2012/01/11/test-yourself-math-jan-11-2012/
This problem is related to worldwide caviar production. What is the total worth of all the caviar produced in the world in one year?
Application Geometry
Math and Computer Animation
This is a clear, concise, and fascinating overview of how some very advanced mathematical ideas are making their way into 3-D animation.
http://www1.ams.org/samplings/feature-column/fcarc-harmonic
Here’s the basic setup. In order to efficiently model a character, you approximate it with a frame that is built around a few important points. To move the character, you focus on moving just those points that define the frame. Thus, moving the character from point A to point B boils down to understanding where those handful of crucial points go.
The tricky part is figuring out a way to smoothly bring all those in-between points along for the ride, and that’s where the math comes in. The secret is to think of those in-between points as averages of the points that define the frame. The article explains how barycentric coordinates, harmonic functions. and a surprising amount of calculus are being used to pull off this movie magic!
Teaching
Writing to Reduce Test Anxiety
This is an interesting report on the effect of writing on test-anxiety.
http://www.insidescience.org/research/1.1885
In one study, a periodic writing assignment improved the scores of women in a college physics course. In another, writing before a math exam improved the scores of high school and college students. In this second study, the most anxious students showed the most improvement.
The nature of the writing exercises is also interesting. In the first study, students were prompted to write something “values-affirming” (i.e., positive) at the beginning of the semester, and again several weeks in. In the second study, students were asked to write immediately before the exam, and they were prompted to write specifically about their anxieties. In both cases, writing had a positive impact for a significant number of students.