XLe CarnavaXL des Mathématiques, #40

I came upon hosting this edition of the Carnival of Mathematics by accident: I asked our august organizer, AXLon XLevy, what had happened to the 40th edition, and he repXLied that he’d had troubXLe finding hosts, and had had no host for it. Did I, he asked, want to host it beXLatedXLy? How couXLd I decXLine?

WeXLXL, then, of course I had to decide whether to caXLXL it the 40th or the 41st. ShouXLd we skip the number that had been aXLXLocated to the missing one? Or should we just caXLXL the missing one “XLate”, and retain its number?

I chose the XLatter, as you can teXLXL. And in honour of that, I’ve scattered a few Roman numeraXLs about this introduction. They’re weXLXL hidden, but I’m sure you’XLXL find them, mathematicaXL adepts that you are.

One more important bit before we bXLast off: AXLon stiXLXL needs hosts, and the hosts need posts, and the posts need authors, and... well, you see the point, yes? PXLease voXLunteer to host a CarnivaXL of Mathematics in the very near future, by sending emaiXL to Alon Levy <alon_levy1@yahoo.com>. And if you write any mathematicaXLXLy oriented posts, submit them to a future carnivaXL using the handy submission form. Thanks muchXLy.

Talking of hosts, the next, 41st edition of the Carnival of Mathematics will be hosted by the folks at the Nazareth College Math Department, in Rochester, NY. Their blog is called “360”, and it’s not officially connected with the college, but it soon will be officially connected with this carnival. Thanks for hosting!

And now... it’s show-time, foXLks!

We’ll start with two items from Mark Dominus, of The Universe of Discourse: Factorials are almost, but not quite, square, and its more expository (and very geeky) follow-up, Factorials are not quite as square as I thought. I’ve always found anything about factorials to be interesting — factorials and Fibonacci numbers; I wonder what the “f” connection is — and you have to like any blog whose domain name is a reference to Adventure.

Skeptic’s Play, by someone called just “miller”, has a two-part item about a tricky dice problem. Part one is Generating functions, and part two is Factoring dice. And look: Fibonacci numbers! Is this eerie, or what?

In Jon Ingram’s blog, Lessons Taught; Lessons Learnt, we get a look at the first book of Euclid’s Elements, including a graph of the relationships between all the propositions, and a discussion of why Jon thinks the Elements are still worth reading: Exploring Euclid’s Elements. And, connecting us back to miller’s previous item, I note that Jon starts his post by mentioning a blog called God Plays Dice.

Back to Fibonacci numbers for a moment, I couldn’t resist including an item from the next Carnival of Mathematics host, the 360 blog, which posts about Fibonacci mileage, observing that for a Fibonacci number Fn (for n > 5 or so), Fn miles is approximately Fn+1 kilometers. The comments carry it a little farther, as well.

Next, Barry Wright III, in 3stylelife, gives us Probability of a Majority Winner (Unit Interval Model). Barry connects mathematics to the U.S. presidential election (but not to dice, nor any f-words).

In The Endeavour, John D. Cook tells us about Binomial coefficients. This kicks off a series of John’s writings on that and related topics, so be sure to click through, and click through, and....

Speaking of a series, we’ll finish with a couple of ongoing post series. The first is by Mark Chu-Carroll of Good Math, Bad Math, giving an introduction to encryption. He’s tagged them all with the category “encryption”, so you can find them that way, but here’s the series so far:

1. Preamble: Encryption, Privacy, and You
2. Simple Encryption: Introduction and Substitution Ciphers
3. Rotating Ciphers
4. Introducing Cryptanalysis
5. Transposition Ciphers
6. Introduction to Block Ciphers
7. DES Encryption Part 1: Encrypting the Blocks
8. Modes of Operation in Block Cryptography (with an important correction here)

And then editor’s prerogative lets me finish with my own series of posts on paradoxes and other mathematical oddities. That first post points to all the others (and I’ll update it as I add more). The series so far:

1. Paradoxes
2. Zeno’s Paradox
3. Russell’s Paradox
4. The Liar Paradox
5. Paradox: 1 = 0

And as a post-scriptum, I’ll add an article from the New York Times. It’s not a blog, but it should be of interest to readers of this carnival: Gut Instinct’s Surprising Role in Math :

One research team has found that how readily people rally their approximate number sense is linked over time to success in even the most advanced and abstruse mathematics courses. Other scientists have shown that preschool children are remarkably good at approximating the impact of adding to or subtracting from large groups of items but are poor at translating the approximate into the specific. Taken together, the new research suggests that math teachers might do well to emphasize the power of the ballpark figure, to focus less on arithmetic precision and more on general reckoning.

 

And with that, we’ll see all of you next week at 360. If you submitted an entry after about 12 September, look for it there.