The 52nd Carnival of Mathematics is up and it's a good one.

I haven't been paying so much attention to the carnival of mathematics lately, so I've skipped some issues — it seems we're already up to Number 47 (the Star Trek edition).

Two of the entries caught my attention. First, the incenter is the Nagel point of the medial triangle. This was known (and there are many similar ways of deriving one triangle center as a different center of a related triangle) but The Advanced High School Math Project supplies a proof.

And second, Quomodocumque gets into some deep water attempting to count the order-types of planar point sets.

It's carnival time again! The 37th Carnival of Mathematics is now up at Logic Nest. They're taking additional submissions through Sunday evening, too, so if you missed out on getting your post included you still have time, and if you already read the Carnival you should check back for more math.

Jeff Shallit takes his turn at posting Carnival of Mathematics #31.

30th Carnival of Mathematics, now up at The Number Warrior.

Carnival of Mathematics #23: Haiku Edition. From The Math Less Traveled.

22nd Carnival of Mathematics, from Wild About Math!

Carnival of mathematics #21: bar-hopping at last. From the not-so-secret-anymore blogging seminar.

Two recent blog posts give some useful advice about how to make one's mathematical writing clearer:

Tim Gowers tells us to put examples first. That is, don't just include examples (I hope everyone already knows that much), but include them before the more general case rather than as an afterthought. That way, the readers will be able to have something concrete in mind when they work through the more general concepts you're trying to describe. Illustrated by an example, of course. Updated.

God Plays Dice reminds us that Mathematics is not notation, or maybe better that notation is not language. Even when a mathematical concept can be stated unambiguously and concisely using standard symbols, it's often clearer to spell it out in English words instead.

My own advice, which I'm not following in this post, is to use plenty of illustrations. A figure is not a proof, of course, and often it's not even as detailed as a textual example can be, but I think a well-chosen figure can provide a visual intuition that can go a long way towards making a paper more readable. Additionally, those of us with kids know how much more intimidating it can be to read books without illustrations than those with them, even when the text is the same, and I think the same holds true for professional writing. As a rule of thumb, I like to have similar numbers of figures and pages, both in formal papers and in talk slides.

Now I'm wondering where one might go to find longer and more detailed collections of advice like this on mathematical writing. There's the Wikipedia Manual of Style for Mathematics but it's less focused on general mathematical writing and more on the nuts and bolts of ensuring a consistent house style for Wikipedia. It cites books by Higham and Halmos that look more relevant, though.

19th Carnival of Spam Mathematics, from Good Math, Bad Math. Baseball, personal finance, romance, and personal improvement. Or maybe, statistics, number theory, algebra, and math education.

Harvey Mudd College has a Math Fun Facts page; recent entries include articles on unfolding projective planes into rectangles, Wallis' infinite product for π, and Cantor diagonalization. I've linked to them before from my Geometry Junkyard, but now they have an RSS feed, making them that much easier to follow: http://feeds.feedburner.com/MathFunFacts

Carnival of Mathematics 18, from JD2718. He seems to have made quite an effort to dig up relevant posts: as he says, "it's kind of big..."

Seventeenth Carnival of Mathematics, now up at MathNotations.

The 16th Carnival of Mathematics is now up at Learning Computation. From it we learn that secondary-school mathematics is good, research mathematics is bad, and computer science is ugly. Well, but there are significantly more research math (and vaguely computational research math) links than the previous few of these, so that's good.

Math Carnival 10. With a bit of side discussion over whether it's appropriate to continue lumping elementary and advanced math together, or whether any split should wait until there's enough more volume.

Carnival of Mathematics IX: this time it's alphabetical.

A new blog (or, well, new to me; it's been around since January): Mathematical paintings and sculptures, by Vlad Alexeev.

The eighth Carnival of Mathematics, now up on Suresh's geomblog.

The seventh carnival of mathematics, now up at nOnoscience.