We at It’s the Thought that Counts are happy to be hosting the 39th edition of the Carnival of Mathematics. The carnival is published biweekly and includes a wide variety of articles about math — everything from general-interest posts about math in society to advanced technical proofs. This edition has been plagued by some organizational difficulties — many weren’t aware that we were hosting this time, and the Blog Carnival submission form was down — so if you didn’t get your submission in in time, I’d be happy to hear from you and add things to the carnival. Just email me at a@thoughtcounts.net.

Although I study theoretical computer science and my coauthor Z studies physics, our posts here are more often about math and science policy considerations than about specific topics in our fields. I nevertheless couldn’t resist taking this opportunity to pose a clever math problem in honor of the number 39:

39 people are attending a large, formal dinner, which must of course occur at a single, circular table. The guests, after milling about for a while, sit down to eat. It is then pointed out to them that there are name cards labeling assigned seats, and not a single one has sat in the seat assigned to them. Prove that there is some way to rotate the table so that at least two people are in the correct seats.

(update: answer in the comments)

While you’re mulling that problem over, if you’d like to see another with no solution yet posted, head over to Continuous Everywhere but Differentiable Nowhere for one that Sam Shah wrote. It’s based on a problem he found from 1896, and it’s definitely a challenge.

Several of you took the opportunity this time around to teach some math. If you’re looking for advanced and technical math writing, the clear winner this week is Charles Siegel atRigorous Trivialities with a post on algebraic geometry. He’s written about how to explicitly construct curves of arbitrary degree with specified nodes.

Catsynth offers us a taste of knot theory. Knot theory is one of those areas of math lucky enough to have associated with it lots of cool pictures, some of which you can see in this post. There’s also an introduction to some potentially interesting but unanswered questions about prime knots.

There are even more pretty pictures available at Jon Ingram’s blog, Lessons Taught; Lessons Learnt. In “The Joy of Hex,” Jon shows lots of tilings using rotations of a single hexagonal shape, and poses some interesting questions about relationships between the tilings. He also describes how tilings can be a useful educational tool to show students that not all math looks like algebra.

In other educational news, Larry Ferlazzo points out a new website which gives step-by-step instructions for a wide variety of high school math problem types. He also points out the extensive glossary, useful for students learning English along with math.

If you’re still not convinced that the internet provides many great opportunities for teaching and learning math, check out Maria Andersen‘s post on “Teaching from the Online Calculus Trenches.” She showcases the 100 slides she made for a presentation on online teaching software and its promises and limitations.

Speaking of software, there’s a poll going on at Walking Randomly concerning whatmathematical software you would use if you could pick whatever you wanted. These competing software packages generate some fierce and probably irrational loyalty among users, so I’m happy to see a growing collection of opinions. If you feel qualified you should definitely weigh in. Otherwise, check it out to see what might be worth learning.

We’ll close with two posts on math in the Olympics. John Cook at The Endeavor gives us astatistical model of Olympic performance by athletes of different genders. He points out that the difference in performance could be the result of a difference in variability across genders rather than a difference in average ability, and gives a quantitative illustration of this possibility.

Finally, while following the Olympic pole vaulting coverage, Xi at 360 notes a silly consequence of the official USATF system for converting between Imperial and metric units. Apparently, the convention is always to round down, which means that by converting back and forth it’s possible to get hilarious results.

That’s all for now. Don’t forget, we’ll continue to update this over the weekend to accommodate new submissions.

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