Welcome to the 26th (and one-year anniversary) Carnival of Mathematics! (Is it odd that the one-year anniversary comes *after* the Silver Jubilee Edition?) Exactly one year ago tomorrow the inaugural Carnival was posted at Abstract Nonsense. Thanks to everyone in the math blogging community for keeping things going for a full year so far!

As is traditional, we begin with a few comments on the number 26. There are 26 sporadic groups in the classification of all finite simple groups, and 26 letters in the English alphabet. 26 is the only number directly between a square and a cube (proved by Fermat), and it is the smallest number which is not a palindrome, but whose square (676) is a palindrome. It is, however, palindromic in bases three (222), twelve (22). Finally, there is an absolutely astonishing system of 14 Diophantine equations in 26 variables such that the set of primes corresponds to the set of positive integer solutions of the system.

On to the good stuff.

Mike, over at Walking Randomly, writes about Music From Mathematical Constants. Following up on a post here at 360, he uses Mathematica’s SoundNote[] function, along with some clever list processing, to generate sequences of tones from the decimal expansions of π.

In Recounting the Rationals, part IV, Brent (from The Math Less Traveled) continues his series on the Calkin-Wilf tree, which is an elegant way to enumerate the rationals, and its amazing properties. Check out the earlier posts in the series, too.

Maria had a former student ask her for help visualizing complex analysis, so she built a great collection of images and videos for Some Techno-help for Complex Analysis at Teaching College Math Technology Blog.

“Vlorbik vents”, and at the same time wonders, about errors that students commit (such as IDF – Ignore Denominators Fallacy) in Fractions and Student Incredulity and its follow-up Oh, P.S., over at Vlorbik on Math Ed.

Denise at Let’s Play Math gives us a two-fer. In The secret of Egyptian fractions, she recounts a story (available for download as a pdf) of an archaeologist and his family learning about the Egyptian method for reading and writing fractions. As a bonus, we get That’s mathematics, a YouTube compilation of math jokes.

If you’ve ever seen mathemagican Art Benjamin perform, you may have left wondering How does Arthur Benjamin square 5 digit numbers in his head? Sol is more than happy to show you at Wild About Math.

Looking to stretch your brain a bit? Try Praveen’s 5-Digit Number Puzzle at Math and Logic Play.

An eclectic selection from Mark at The Universe of Discourse. First, in Nonstandard adjectives in mathematics we see that while a toy fire engine is not actually a fire engine, a toy ball is indeed a ball; this doesn’t appear to happen very often in mathematics. Major screwups in mathematics: example 1 presents the first in what we hope will be a series on results that were believed (by many) to be true, in this case for 30 years, but were eventually proven false. Finally, Mark uses Ramanujan congruences to remind us all of just how awesome math can be.

Last, but certainly not least, MathNotations‘ Dave shares a Fascination with Pyramids again…, a problem appropriate for geometry students. He is also conducting a survey in Why a Poll? Why Now? A Significant Sample…, and he would really appreciate your input on the teaching of algorithms. The poll is open until February 29, so head on over and share your thoughts.

(If anyone has a late submissions they’d like to send, go ahead – I’ll gladly post an update later today if necessary.)

The next Carnival is scheduled for February 22, but needs a host. If you’d like to volunteer, head over to Carnival of Mathematics and tell Alon.

**Update 2/13: **The Feb 22 Carnival will be hosted at JD2718.