## Carnival of Mathematics #22

Welcome everybody to the 22nd Carnival of Mathematics!

This edition has 16 articles and 16 is my lucky number. Very cool!

If you find these Carnivals enjoyable please spread the word and help the *blathosphere* (Math+blogosphere=blathosphere - thanks Vlorbik for this reference to the term) grow by linking to this and every Carnival and by adding Math-related blogs to your blogroll. If you're not on my blogroll and your blog has predominantly Math-related content let me know and I'll add you.

So, I whined a little while ago that 22 is a pretty difficult number to make a theme around. Heather, from the 360 blog community provided me with the following fascinating trivia about the number 22, including a *startling coincidence*.

"You could make use of the startling coincidence that the 22nd State (Alabama) was admitted to the Union on December 14, the very day of the Carnival! This was 188 years ago, which is not a multiple of 22 [although 88 is].

If that doesn’t help, and I can’t see how it would, check out

Adam Spencer’s Book of Numbers. The number 22 is:

* the approximate circumference of a circle of diameter 7

* the 3rd pentagonal number (after 1, 5, and 12)

* palindrome-happy (I made that word up). Not only is 22 a palindrome, but so is its square 484

* well known for its appearance in Joseph Heller’sCatch-22

What's Special About This Number states that:

22 is the number of partitions of 8.

Well, I give up. The only consolation I have is that when Brent hosts the next Carnival at The Math Less Traveled he's going to have to try to come up with a theme for the number 23. If Heather can't help him then he can use this exciting piece of trivia from What's Special About This Number:

23 is the smallest number of integer-sided boxes that tile a box so that no two boxes share a common length.

Anyway, on to the festivities!

[ Note: Several of you sent me more than one submission so, as editor, I picked one to publish. Please submit the ones I didn't publish to future Math Carnivals. Thanks. ]

**Rich Cochrane** presents Irrational Numbers And Measurement posted at Big Ideas, saying, "Not sure if this is a bit too basic, but thought you might enjoy it anyway."

Basic is good and basic can go very very deep. Wild About Math! is all about basic. Understanding rational vs. irrational numbers is an important concept. I remember the excitement I felt when I learned a proof that the square root of two was irrational.

**Kalid Azad** presents How To Measure Any Distance With The Pythagorean Theorem posted at BetterExplained, saying, "Hi Sol, I saw you were hosting the carnival this time and thought it'd be fun to submit :). This article is on generalizing the Pythagorean Theorem, and using it for problems other than geometry. I really like the philosophy on your site -- I'm wild about math too :). Take care, -Kalid"

This is a great article and an awesome blog. This article will really stretch your thinking about what the Pythagorean Theorem can be used for and it is "better explained." Nice!

**Larry Ferlazzo** presents HippoCampus For History, Government & Math posted at Larry Ferlazzo's Websites Of The Day For Teaching ELL, ESL, & EFL.

This is a nice review of the HippoCampus web-site which provides textbook and course material in Algebra, Calculus, and other (non-Math) subjects.

**Mark Jason Dominus** also presents The Universe of Discourse : Four ways to solve a nonlinear differential equation posted at The Universe of Discourse

This is a nice exploration for graduate students working on non-linear differential equations.

**Aaron Roth** presents Smoothed Analysis of the Price of Anarchy posted at Adventures in Computation, saying, "This entry provides an introduction to computational game theory and the "price of anarchy". It then discusses a recent technique for giving a "smoothed analysis" of the price of anarchy of a simple game, and examples."

I think Aaron pretty clearly explains what his article is about.

**Andree** presents A Merry Binary Christmas posted at meeyauw, saying, "This post describes what we do in my middle school classes for the holidays."

Andree guides readers on a great exploration of a simple and fun Math trick. I wrote a very simple version but Andree's variation, elaboration, and exploration is well worth reading.

**Graeme Taylor** presents Understanding Public Key Cryptography with Paint posted at Modulo Errors, saying, "An introduction to public key encryption and Diffie-Hellman key exchange; notes from a talk prepared for 16 year old school students."

This is a very accessible article about a topic that is hard to grasp for many people. Nice writeup!

**Denise** presents Word problems in Russia and America posted at Let's play math!, saying, "Link to an Andrei Toom article about the importance of word problems as mental manipulatives---a must-read for math teachers."

This is a great find, a reference to an article (essentially a book) about Math education written by a Russian mathematician. As you might imagine his thoughts about the American attitude towards mathematics are not pretty. But, I agree with Denise - a must-read for math teachers, and for others of us too.

**David Eppstein** presents The topcoders count isosceles triangles posted at 0xDE, saying, "Analysis of the number of different isosceles triangles in a grid, up to translational equivalence."

This articles discusses an interesting geometry problem and how to approach it via computer programming. While I couldn't really grasp the computational geometry here I like that the problem discussed is simple and very elegant.

**Julie Rehmeyer** presents Mathematical Police Find Security Bug posted at MathTrek.

This is an interesting article about how a bug in a computer chip could cause vulnerabilities with the RSA encryption algorithm leading to serious security problems.

**Matt** presents Beauty in Mathematics posted at 360, saying, "Having trouble with the submit form. I hope this gets through."

Yes, happily your submission got through. This is a thought provoking article. If you spend any time wondering about what beauty in mathematics is about you'll enjoy this article.

**Eric Macaulay** presents Maths for Mortals posted at Maths for Mortals, saying, "For those who enjoyed the first Portia problem, here's another!"

A fun logic problem: simple, elegant and fun.

**jd2718** presents Little probability quiz posted at JD2718, saying, "I wanted to give you something. Sorry it's not more interesting."

No need to apologize. One man's uninteresting is another man's fun. Anyway, this is a nice set of questions on basic probability.

**Vlorbik on Math Ed** presents Careful Now: 21st Century Edition posted at dy/dan, saying, "this *isn't* by me ... i didn't do anything very interesting this fortnight .... but it sure as heck deserves the exposure! "vlorbik nominated this outstanding piece on the role of high tech in math ed by dy/dan" ... words to that effect ... or leave me out of it ... whatever suits your taste. my url is of course http://vlorbik.wordpress.com . here's looking forward to a great carny! (which i won't see until next week ... vacation, don'tcha know ...)"

If you've ever tried to get Math formulas or symbols into a blog posting you'll get a chuckle out of this.

**Beans** presents The League of eCcentric Mathematicians posted at Me Or My Maths, saying, "You don't really have to put this in, but I found it funny (understandable for a teenager) and thought others might do to. [It feels weird submitting this!]"

Hey, don't feel dumb, unless you want to! This is a cute two act play about eccentric mathematicians, written for those of us with short attention spans.

**Mike** from Walking Randomly presents A tricky little integral.

This is a nice little article about taming a tricky little integral that MathCAD couldn't simplify.

Well, that concludes this edition. Submit your blog article to the next edition of **carnival of mathematics** using the carnival submission form. Past posts and future hosts can be found on the blog carnival index page.

Next month's host will be Brent will be Brent at The Math Less Traveled.

IsabelDecember 14th, 2007 - 15:54

I feel obliged to point out that Mark Dominus’ post on differential equations is really undergraduate-level. I came very close to presenting it to my freshmen — who certainly could have understood it. (Alas, I didn’t have the time.)

SolDecember 14th, 2007 - 16:58

Isabel, you’re right, of course. Brain cramp on my part.

I don’t like to change posts unless the errors are life threatening so I’ll let the error stand with your correction duly noted.

Thanks for catching it.

Mark DominusDecember 15th, 2007 - 22:09

I’m glad you both agree that it is undergraduate-level. The mischaracterization had been bothering me, because I try to target my articles to an imaginary audience with about one year of college calculus, and I didn’t think I had missed the mark by so much this time.

SolDecember 16th, 2007 - 16:19

Mark,

I took Differential Equations as an undergrad. That’s why I realized it was a brain cramp.

Sol