It has become tradition, at the start of each Carnival of Mathematics, to discuss the number of the Carnival. And here I was, all set for 48, not realizing we’d gone off cycle by a week. (Really, I was kind of hoping for 45. I hosted 9, 18, 27, but missed 36…). (Also, 44 would have been cool. My age. # of the new president…)

47 is more impressive in geeky popular culture than in mathematics. Forty odd years ago something of a cult of 47 developed at Pomona College, devoted to noticing occurences of the number, the digits in that order, multiples, etc. Looking for 47s, they found them.

So, what grabs your attention? 47 is of the form 3n – 1 (yawn). It is odious, it is a lucas number, it is a safe prime? The Pythagorean Theorem is the 47th in Euclid’s elements (but something had to be 47th. And something else 48th, right?). Or the outrageous claim that 47 is the quintessential random number…? Or, even better/worse, the recurrence of 47, the string 47, multiples of 47, and even apartment 4-g in just about every episode of Star Trek: The Next Generation, and each of the spin spin off offs that followed?

Today, all hands, the Carnival of Mathematics is going where, well, hm. Sorry. I’ll limit it to headings.

Wesley Crusher (or how we teach our young)

Dave Marain at MathNotations has a wonderful new math contest for high school (and middle school) kids. Sign up is free. The contest is online, probably February 3. Kate at f(t) found that her students were more interested in bouncing a ball than studying exponents, so they studied the bouncing ball. (with solution). Pissed off Teacher is preparing her students for the AP, an exam with different mechanics.

Jason, the Number Warrior, turns factoring quadratics into a graphic puzzle. Rolfe introduces his sons to binary. Check out this interesting graph of arithmetic knowledge and self-esteem (ouch).

Vulcans (hard stuff)

Rod calculates the distance between two lines in $\mathbb{R}^n$. David (0xDE) compares two ways of looking at a seating problem (ménages problem). At Quomodocumque we read about a leftover problem: n points in the plane with no 3 collinear. Brent of Math Less Traveled calculates Pi through looking at the integer part of its multiples, and gains digits more quickly than it initially seems likely.

And in the category of “if the pictures look so simple, why is the counting so hard?” David (same as above) describes how several families of combinatorial objects can be generated as the collection of complete subgraphs of a graph.

A New Season

Denise at Let’s Play Math celebrates the new year with the 2009 game. Mike at Walking Randomly explores “What is interesting (mathematically) about 2009” And twopi at 360 (come on, you have to smile for that, right?) has both interesting and trivial exploration of the number 2009.

To boldly go… (new work, exploration)

The Carnival of Mathematics features a first: Polymath has blog-published what looks to be an original piece of work: a new proof in plane geometry. The existing proofs are more complicated, and involve trig. Foxmaths seems preoccupied with calculating values that exist, and some that don’t. The value of omega: $1 = \omega \times e^\omega$ exists, but it takes so long to find! The solutions to $F^1 = F^2$ (when we ignore the leftmost digits of F)? The sum of the sin(1) + sin(2) + … + sin(n)?

And Jost a Mon explores the mathematics of sprinting

The Prime Directive

Zeno of Halfway There is all over bad analysis of the problems with the election in Minnesota. And he has a photo of Spock (scroll down). Edmund at Maxwell’s Demon discusses the responsibilities of mathematicians. Political Calculations uses math as a tool to help you: math can help with a little analysis of the unemployment rate? Perhaps. But math certainly can help plan your wedding invitation list. Twopi catches a pop star misnaming variables.

The Holodeck (Games and puzzles and recreational stuff.)
(I thought about calling this one “dabo” but, seriously, who watched DS9?)

Poker with Venn Diagrams? Read the post, then click Mike’s solution (at Critiques of Libertarianism). My submission is a little dice puzzle. People find conditional probability sooo frustrating.

Enterprise (history and old stuff and strange stuff)

Michi on the Chromatic Number of Lichtenstein. John Kemeny has photos of mathematicians … and more of the same … but is looking for their names. They come from Time/Life’s archives. Ξ at 360 found some polygons in the Smithsonian. Any with 7 sides? Look at the photos closely. Vlorbik is having some issues with WordPress’ implementation of TeX.

James T Kirk (for laughs…
and anything else that can’t be taken too seriously)

Ian at Logic Nest recounts some amazing facts demonstrating the amazing intelligence of Karl Gauss, for example, did you know it only takes Gauss 4 minutes to sing “Aleph-Null Bottles of Beer on the Wall”? (silly, but very funny. Don’t skip it.)  The images below are from Blig Blug and Friends and (x or why) [seems to have wandered off. But the link remains, and is worth it]. Click the images [or non-image] to see more of their math-related (and non-math related) cartoons.

Fantasy Island

If you submitted via the carnival tool, and your submission is not here, well, the tool was broken. Sorry.
The next carnival is due January 30… but I don’t know where. If you are host, link back so that readers might track you. And if you are a reader, watch the comments here, or keep an eye out at the Carnival of Mathematics webpage.

All good things…

1. January 18, 2009 am31 4:14 am 4:14 am

Great job, Jonathan despite all the glitches! We can always expect something different and creative from you particularly in the way you categorize the offerings and this Carnival did not disappoint. BTW, ’47 has some significance for someone I know!

2. January 18, 2009 am31 4:44 am 4:44 am

Sorry, Jonathan, just a few more thoughts…
The Math Contest I’m running at MathNotations is for Middle School and HS students with about half the questions appropriate for both groups. With a team working on the problems, most groups can complete the questions in 45 minutes even though extra time is provided. Registration closes in about 10 days and we’re even receiving interest from schools in the UK. The international flavor is great!
Thanks again for mentioning this!

3. January 18, 2009 am31 6:57 am 6:57 am

Just finished watching through every episode of DS9, in order. It’s much better than I remembered because I originally saw the episodes more or less at random. There’s a lot of continuity and sneaky tricks like minor characters blossoming into major characters — things you don’t catch watching episodically. And unlike certain current TV shows with continuity, everything falls together by the end in a logical fashion.

• January 18, 2009 am31 10:27 am 10:27 am

Did you start before the carnival was published? Are you kidding? Sisko was the most overacted Captain since Kirk, especially the first season. Although Munroe should have dropped a reference to the Jem Hadar for the current comic…

Damn, I think I watched more of the stuff than I should admit.

4. January 18, 2009 pm31 5:07 pm 5:07 pm

I love how you set up this Carnival! And it’s sad that I put actual time into thinking, “I’m glad he didn’t put us in ______’s section” and “But wouldn’t it have been cool to be in _______’s section.”

I’m also going to admit that it wasn’t until you made the 360 and TwoPi comment that I realized that THAT was why TwoPi chose his username. It had never, not once, occurred to me.

5. January 19, 2009 am31 6:21 am 6:21 am

Took about six months of viewing.

I agree 1st season was inadqueate.

Captain’s acting didn’t bother me.

6. January 19, 2009 pm31 10:09 pm 10:09 pm

Thanks for the link. I’m currently experiencing some problems with the images which were uploaded in the last few days. It could be that I’m getting extra hits or it could be a problem with Geocities. In either case, the backup site to see the images is http://xwhy.comicgenesis.com

All are welcome to drop by and comment.

7. January 20, 2009 am31 3:20 am 3:20 am

And I thought you’d pulled the image. Sorry, and thank you for dropping by. I’m glad I discovered your work, lots of fun!

8. January 20, 2009 am31 4:00 am 4:00 am

Thanks. I don’t think it had anything to do with your site. Just a co-incidence. I had to upload those images again, so the problem had to be with geocities.com.

Everything seems to be back to normal now.