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/2011/10/03/test-yourself-math-oct-3-2011/
This question is based on Facebook’s claim that they have 800 million users, and asks “What percentage of the world’s population uses Facebook every day?”
This is a great set of photos depicting art made from the paths of Roomba robotic vacuum cleaners:
The paths traced out by these self-starting sweepers could provide a novel approach to random walking. And I wonder how much of the movement algorithm can be reverse-engineered simply by looking at a collection of paths?
It might be fun to perform experiments with roombas. For example, we could try to determine how long it takes one to completely traverse a floor, or how many times on average they pass through a given point. Or if working in tandem, what is the probability that two roombas collide?
Of course, we’d have to address the ethical issues of experimenting on roombas without their consent.
I recently had some fun with one of my favorite triangles. It all started with this innocent NY State Regents Exam question:
In triangle ABC, we have a = 15, b = 14, and c = 13. Find the measure of angle C.
This problem is designed to test the student’s knowledge of the Law of Cosines, but because of the special nature of the 13-14-15 triangle, it’s easy to find angle C without it.
And since it was a multiple choice question, I considered another approach. I constructed an equilateral triangle with side AB and produced the following diagram:
Before I actually performed the construction, I assumed that third vertex of the equilateral triangle would lie in the interior of the original triangle ABC. By the construction above, it appears to be outside triangle ABC.
So here’s the challenge: prove that the third vertex of the equilateral triangle lies inside triangle ABC without using the Law of Cosines!
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/2011/09/07/test-yourself-math-sept-7-2011/
This question comes from an article about the proliferation of expensive summer camps catering to wealthy clientele. How much does a day of high-end summer camp cost?
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/2011/08/31/test-yourself-math-aug-31-2011/
This question is based on a recent report tying U.S. Census data to consumer spending. Approximately how much is spent on back-to-school clothing per student?