Aha!

That moment of sudden insight: you see how to solve a problem that you’ve been struggling with. Last week on Scientific American‘s website there was a two-page article about research that analyzes what is going on in the brain during that moment.

Love Shaq?

As reported in Bob Matthews’ Sports Exchange Blog (affiliated with the Rochester (NY) Democrat and Chronicle newspaper), Shaquille O’Neal of the Miami Heat NBA team is in the midst of a divorce.  Details of his monthly expenses have been leaked to the press.  Some of the numbers are rather interesting: 

Writing Review Sheets

I was re-reading the post Writing Tests recently, and thinking about how I prepare for exams. In particular, I was thinking about how I prepare students for exams, and one way that has worked well for me is giving an Outline of Topics as a review sheet.

Musical Pi, Part 1

Jon Turner, a professor of musical composition here at Nazareth, has composed a suite of music based on π! (see also part 2 and part 3) As he says:

The basic idea is to use the decimal expansion of pi to give an unendingly varying [but] related series of notes.

The first step was to convert π to base 12 (to match the chromatic musical scale), so

(where B represents decimal 11 in base 12). Starting with C at 0, he gets

The Silver Jubilee Carnival!

The 25th Carnival of Mathematics is up: the Silver Jubilee Edition! It’s over at Walking Randomly, a 5-month-old blog that touches on mathematics, physics, vintage computing, linux, pocket PCs, music and programming. We’ve linked to them before, on their post What is interesting about the number 2008? but I’m also partial to their recent posts Mathematics on the Pocket PC and their posting of this comic below by xkcd (click on the comic for a legible version):

This edition of the Carnival (which, yes, we were just talking about) contains a dozen interesting entries, so go take a peek!

Friday Software Review: Texify

Have you ever wanted to include mathematics on your website (or in a blog post, or in a forum, or…)? If you know how to use LaTeX, you can do just that, and make it look purty, too.

Math Helps College Students

According to the August 4, 2007 issue of Science News (Vol. 172, No. 5, p.78), the more math and science classes students take in high school, the better they perform overall in college (emphasis mine):

Apparently, high school math is the key to good grades in college science classes.

A survey of more than 8,000 students from 74 colleges found that each additional year of high school math correlated with a 1-to-2-point advantage, on a 100-point scale, in college chemistry, physics, and biology grades. For example, 2 additional years of high school math typically corresponded to a 3-point improvement in college biology—the difference between, say, a B+ and an A-.

Kids who took more high school classes in chemistry, physics, or biology gained a similar edge when they took a class within the same discipline at the college level. However, no significant benefit crossed a line between science disciplines. Only math seemed to boost grades in other subjects. The study appears in the July 27 Science.

Coauthor Philip Sadler of Harvard University says that students who take advanced high school math classes are better able to handle the more basic math required in college science classes.

The results are “not surprising,” says James Milgram, a Stanford University mathematician and a member of a presidential panel advising the U.S. Department of Education. He points out that decadal surveys by the department have shown that as more students have taken advanced high school math classes, their chances of graduating from college have improved. “There is overwhelming evidence that the single most important factor that correlates with success in college is what is done in high school math,” says Milgram.

(Hat tip to Brian Witz.)

A Matter of Perspective

Sunday’s F Minus (click for full size):

Philip Rivers and Calculus

Philip Rivers, quarterback for the San Diego Chargers, has been in the news recently because of his knee. But only a year ago he was at Sports Illustrated talking about Calculus:

I’m a math guy. Calculus, all that stuff. My favorite subject in college [N.C. State] was statistics. Some people would be like, Gosh, I hate this stuff, but I used to get fired up trying to figure out a problem. I get my math from my mother [Joan]. She was a competitive swimmer and a math teacher. Me and her, we had a blast doing calculus stuff.

For the whole article, including a great picture of Rivers doing calculations on a clear board, check out First Person from January 9, 2007.

A Sudoku-Solving (Quantum) Computer

So you bought a Sudoku Lotto ticket and now you’re having trouble solving it? Turn to a quantum computer! When D-Wave Systems, Inc. announced that it had created a 16-qubit quantum computer last year, they demonstrated its power in three ways: “searching for molecular structures that match a target molecule, creating a complicated seating plan, and filling in Sudoku puzzles.” (See First “Commercial” Quantum Computer Solves Sudoku Puzzles). According to D-Wave’s website, two months ago they unveiled a 28-qubit model; however, there’s no mention of its game playing skills.

For more about Quantum Computers, see How Stuff Works.

Juxtapositions: Sudoku Lotto

There I was, a mathematician in the grocery checkout line. Inexplicably, I found my eye drawn to the scratch-off lottery ticket machine. Unlike the proverbial punk in a Dirty Harry movie, I did feel lucky, and I surreptitiously slipped a couple bucks out of my wallet, hoping the cashier wouldn’t notice and take me for a fool.

One of the current scratch-off games offered by the New York Lottery is a SuDoKu game.

Money Money Money

Just so you don’t think that the Harry Potter game is the only place to find cool polygonal coins, here’s a question for you: what shape is the Susan B. Anthony dollar? Yes, it’s round, but if you look more closely you’ll see the outline of a regular hendecagon — an 11-sided polygon!

Heptagons in Harry Potter!

A few nights ago my four-year old pulled out a Harry Potter game in which Hagrid and Harry collect tokens and buy up school supplies in Diagon alley, all the while trying to avoid bumping into Malfoy. We opened it up, and lo and behold I noticed for the first time that several of the tokens are regular heptagons! So much for my theory that heptagons are hard to find.

EdHeads at the STEM Blog

There was a great resource posted yesterday at the the STEM Blog (Discussions in Science, Technology, Engineering, & Mathematics Education): Are you an Edhead? This post directed people to the site Edheads.org, which features activities on investigating a car crash, performing surgeries, predicting the weather, and more. What impressed me when I visited the site was the level of detail in the activities: the car crash investigation walks visitors through the process of collecting data and applying it to mathematical equations, while the hip surgery gave more surgical steps than I would have expected, with optional photos as a bonus. Be warned: even in cartoon form, if you are squeamish about surgery then this isn’t the activity for you, although our seven-year-old declared it AWESOME! and I found it to be pretty cool myself. All of the activities come with teacher’s guides and grade level suggestions.

Thanks to the STEM Blog (a brand new blog — even newer than us!) for bringing this site to our attention.

The “Law of Probabilities”

This Pearls Before Swine strip appeared on December 29, 2007 (click for full size):

For a related discussion, see the Infinite Monkey Theorem.