NES/MAA Meeting

The NES/MAA meeting I mentioned in my last post was held at Salve Regina University, which is located on the grounds of an opulent mansion on the ocean at Newport Rhode Island. There were a number of interesting invited presentations. I particularly enjoyed the talk by David Abrahamson and Rebecca Sparks on Baseball Statistics and Keith Conrad's talk on Check Digits (in credit card numbers, etc.). Both dealt with fairly elementary mathematics, but related the results to the everyday world in a compelling way.


Ed Burger's Battles Lecture on p-adic norms was a bit more technical, but Ed's high-energy and humorous style of presentation made the medicine go down very well.

My presentation on The Pythagorean Theorem (Revisited) was well received. I was a bit surprised and gratified that none of the mathematics professors or students previously knew the main theorem I was presenting, the Pythagorean Theorem for right tetrahedrons.

Presentation at NES/MAA Meeting, June 12

I will be attending the New England Section of the Mathematical Association of America meeting in Newport Rhode Island, June 11-12. I have had a paper accepted. It is an expository paper presenting some simple and interesting facts relating to the Pythagorean Theorem that many professional mathematicians do not know. To view my notes for the presentation, go to http://www.scribd.com/doc/32536190/Pythagorean-Theorem-Notes.

Comments on the paper are welcome.

Coded arithmetic puzzles

In a course I am developing, I want to give out some math problems for people to work on that should be in the grasp of adults without much math background at all. One such problem is what I call "coded arithmetic puzzles". The commonest example I know is "Send More Money": Solve S E N D + M O R E = M O N E Y, where each of the 8 different letters in the equation represents a different digit.

I would like to find a collection of these types of puzzles that would enable me to give different classes different puzzles. The puzzles should not be too tedious and should not require too much cleverness; in other words of the difficulty of Send More Money, or easier. Perhaps someone has written a program that would generate puzzles of this sort.

Does anyone know if there is a formal name for this type of problem? "Coded arithmetic puzzles" is not a very helpful Google search.

Name Change

Cambridge Math Learning, Inc. is now doing business as Math for the Rest of Us. I think this emphasizes the mission of the company, which is to teach mathematics to the "bottom 80%" of adult math learners; those who have been poorly served by mathematics instruction in the past and most of whom now have anxiety when facing mathematics that they must learn.

More on Ordering a Multiset

I posed problem A3, to find a formula for the k-th largest element of an n-element multiset A. I found a very interesting formula that is unknown to several famous combinatorists, including Donald Knuth, and I have submitted a problem to the MAA Monthly Problems section which asks for the solution that I found, a linear combination of certain symmetric functions. However, Knuth told me that there is a simpler known formula of a different type. Knuth's formula is

min(max_k)

where (max_k) is a set of C(n,k) numbers, each of which is the maximum of a different subset of A of size k.

Pretty cute!

Mandelbrot Set

A friend just sent me a link to a fantastic video: Mandelbrot Fractal Set Trip to e214 by teamfresh. The video runs about 9 minutes and zooms in on the Mandelbrot set to a magnification of 10^214. Wow!

It feels like there must have been some pretty clever programming and lots of computer time used to produce this video. The idea of using video to zoom in on the Mandelbrot set is so powerful that it seems to make the beautiful still pictures that I am familiar with, obsolete. To teamfresh, I say Bravo!

I am amazed and humbled by the incredible complexity that can be contained in the simplest mathematical formulas, as shown in this video. Truly our own inventions can take a life of their own.

E17. A 1-2-3 counting problem

The following problem seems at first to be quite difficult, but if you look at it the right way it isn't.

How many n-digit integers are there that contain no digits other than 1, 2, or 3, subject to the condition that any two consecutive digits differ by exactly 1.

This problem (for the n = 10 case) appeared in the ATMIM newsletter, Winter 2002, where it is credited to http://www.mathkangaroo.org, an interesting math enrichment and contest Web site.

I think this problem is too easy for me to post an answer, but if anyone asks for one, I will.