The Carnival of Mathematics: No. 28

Tyler and Foxy's Scientific and Mathematical Adventure Land is proud to present the 28th. Carnival of Mathematics! According to the treasured tradition of this fine event, I will exposit something interesting about the number 28. Fortunately, I got the perfect number to do so, literally. 28 is a perfect number, such a thing being defined as the sum of its positive divisors that are not equal to the number itself. That is, 28 is the sum of 1, 2, 4, 7 and 14. The next guy who gets to talk about perfect numbers will be the guy who happens to be doing the 496th. Carnival of Mathematics. Good luck, whoever you end up being!

And now, on to the good stuff...

Over at The Universe of Discourse, Mark Dominus provides us with three interesting posts. The first concerns an interesting property in the world of coding theory known as "unique decodability", or whether particular strings are the result of unique encodings. The second is on rational roots of polynomial equations. The third concerns techniques of algebraic manipulation that work...sometimes.

From the website Old-Wizard dot com, we have this list of the top 10 Mathematicians of All Time. In my mind, they get it mostly right. The only serious problem I can see is that Leibniz is nowhere to be found. Seriously, WTF?

My esteemed blogmate Foxy over at Foxmaths 2.0! provides us with this post on an interesting geometric question: can you divide a cube into a finite number of smaller cubes, all of different sizes? The answer is....just kidding, I'm not a spoiler. Go read!

Charles Daney at Science and Reason sends us this post on important concepts in algebraic number theory, in particular concepts from ring theory. The key concept is that of the "Dedekind domain", a specific type of commutative ring in which every nonzero ideal can be uniquely factored into a product of prime ideals.

Over at The Number Warrior, Jason Dyer provides us with this fascinating historical discussion of the ancient Egyptian calculation of pi. It even has tables of Egyptian numeric characters showing the development of the quantity over the years, I think that's pretty damn neat.

Julie Rehmeyer provides us with two posts on Sophie Germain, the first person ever to lay out a realistic plan for rigorously proving Fermat's Last Theorem, one of the peskiest little assertions in the history of number theory.

In the math education and pedagogy category, Mr K. over at Math Stories sends us this entry on how overemphasis on mechanical shortcuts over conceptual understanding harms long term learning in mathematics.

Over at Wild About Math!, we have a probability puzzle, apparently the first in a regular series untitled "Monday Math Madness".

In the aesthetics of mathematics category, we recieve this entry from Art Black, which compares the perception of beauty of mathematics to the perception of beauty of music.

The winner in the terms of sheer volume of material for this edition of the Math Carnival is Blake Stacey, who sends us a series of five posts on supersymmetric quantum mechanics! [1, 2, 3, 4, 5]

And finally, at the Teaching College Math Technology Blog, we recieve this entry from Maria Andersen on software for teaching math courses online.

And that's all, folks! It has been a pleasure to host this event, and I hope I have done so to your satisfaction. Good luck, and godless speed.