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:
http://learning.blogs.nytimes.com/2010/11/17/test-yourself-math-nov-17-2010/
This question was based on a new world record in computational speed set by a Chinese supercomputer. We’ve officially fallen behind
I recently attended a function at the Museum of Modern Art hosted by Math for America. In typical MfA fashion, the invitation was designed around a relevant mathematical idea, in this case, the Art Gallery problem.
The Art Gallery problem (aka the museum problem) basically asks “What is the minimum number of guards required to keep an entire region under watch?”.
We make the usual idealizing assumptions for the purposes of elegant mathematics. For instance, we assume that the guards can see infinitely far, that there are no obstructions (other than the walls), that the guards can see everything in front of them, and the like.
So looking at the map at the right, how many guards would be needed to watch over the fifth floor at the MoMA?
The Art Gallery problem is a classic question from computational geometry, and its solution involves a lot of great ideas from graph theory and graph coloring.
There are a number of fun extensions to this problems, too, including the watchmen route problem (one watchman guarding the entire museum) and the fortress problem (guarding the exterior, rather than the interior).
The Art Gallery problem is the best kind of math problem: easy to state and understand, surprisingly rich and complex, and lots of fun to play around with!
This article offers a nice introduction to the Riemann Hypothesis, one of the mathematics problems eligible for the Millennium Prize.
Solve it, and you’ll earn yourself one million dollars! If you do solve it, I’d be happy to look it over before you submit your proposal to the committee. Just send it my way and I’ll get back to you shortly.
If finding zeroes of the Riemann Zeta function is asking too much, the author offers up a classic problem in elementary number theory at the end of the article–something anyone with a few minutes to spare and a calculator can dive into. It’s a surprisingly serious result, with a surprisingly easy solution!
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:
http://learning.blogs.nytimes.com/2010/11/10/test-yourself-math-nov-10-2010/
I was excited to bring the principle of Inclusion and Exclusion to one of these Times problem, even if it is a simple example.
My colleague, Scott Matthews, offered a very elegant solution to the Coffee and Cream mixture problem in response to the straight-forward solution I put forward. As he commented:
In the end, both cups have the same amount of liquid. Therefore, by the simple law of displacement, the amount of cream in the coffee is the the same as the amount of coffee in the cream.
This is a really nice way to think about the problem. In the end, the “coffee” cup contains the same amount of liquid as it started with. Therefore, any cream that ends up in the “coffee” cup had to displace some coffee.
Where did that coffee go? It ended up in the “cream” cup! Here’s a visual interpretation.
Thanks, Scott, for the elegant solution!
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