My Mathematics Reading For The 13th of June


I’m working on the next Why Stuff Can Orbit post, this one to feature a special little surprise. In the meanwhile here’s some of the things I’ve read recently and liked.

The Theorem of the Day is just what the name offers. They’re fit onto single slides, so there’s not much text to read. I’ll grant some of them might be hard reading at once, though, if you’re not familiar with the lingo. Anyway, this particular theorem, the Lindemann-Weierstrass Theorem, is one of the famous ones. Also one of the best-named ones. Karl Weierstrass is one of those names you find all over analysis. Over the latter half of the 19th century he attacked the logical problems that had bugged calculus for the previous three centuries and beat them all. I’m lying, but not by much. Ferdinand von Lindemann’s name turns up less often, but he’s known in mathematics circles for proving that π is transcendental (and so, ultimately, that the circle can’t be squared by compass and straightedge). And he was David Hilbert’s thesis advisor.

The Lindemann-Weierstrass Theorem is one of those little utility theorems that’s neat on its own, yes, but is good for proving other stuff. This theorem says that if a given number is algebraic (ask about that some A To Z series) then e raised to that number has to be transcendental, and vice-versa. (The exception: e raised to 0 is equal to 1.) The page also mentions one of those fun things you run across when you have a scientific calculator and can repeat an operation on whatever the result of the last operation was.

I’ve mentioned Maths By A Girl before, but, it’s worth checking in again. This is a piece about Apéry’s Constant, which is one of those numbers mathematicians have heard of, and that we don’t know whether is transcendental or not. It’s hard proving numbers are transcendental. If you go out trying to build a transcendental number it’s easy, but otherwise, you have to hope you know your number is the exponential of an algebraic number.

I forget which Twitter feed brought this to my attention, but here’s a couple geometric theorems demonstrated and explained some by Dave Richeson. There’s something wonderful in a theorem that’s mostly a picture. It feels so supremely mathematical to me.

And last, Katherine Bourzac writing for Nature.com reports the creation of a two-dimensional magnet. This delights me since one of the classic problems in statistical mechanics is a thing called the Ising model. It’s a basic model for the mathematics of how magnets would work. The one-dimensional version is simple enough that you can give it to undergrads and have them work through the whole problem. The two-dimensional version is a lot harder to solve and I’m not sure I ever saw it laid out even in grad school. (Mind, I went to grad school for mathematics, not physics, and the subject is a lot more physics.) The four- and higher-dimensional model can be solved by a clever approach called mean field theory. The three-dimensional model .. I don’t think has any exact solution, which seems odd given how that’s the version you’d think was most useful.

That there’s a real two-dimensional magnet (well, a one-molecule-thick magnet) doesn’t really affect the model of two-dimensional magnets. The model is interesting enough for its mathematics, which teaches us about all kinds of phase transitions. And it’s close enough to the way certain aspects of real-world magnets behave to enlighten our understanding. The topic couldn’t avoid drawing my eye, is all.

My Mathematics Blog, As March 2015 Would Have It


And now for my monthly review of publication statistics. This is a good month to do it with, since it was a record month: I had 1,022 pages viewed around these parts, the first time (according to WordPress) that I’ve had more than a thousand in a month. In January I’d had 944, and in February a mere 859, which I was willing to blame on the shortness of that month. March’s is a clean record, though, more views per day than either of those months.

The total number of visitors was up, too, to 468. That’s compared to 438 in January and 407 in short February, although it happens it’s not a record; that’s still held by January 2013 and its 473 visitors. The number of views per visitor keeps holding about steady: from 2.16 in January to 2.11 in February to 2.18 in March. It appears that I’m getting a little better at finding people who like to read what I like to write, but haven’t caught that thrilling transition from linear to exponential growth.

The new WordPress statistics tell me I had a record 265 likes in March, up from January’s 196 and February’s 179. The number of comments rose from January’s 51 and February’s 56 to a full 93 for March. I take all this as supporting evidence that I’m better at reaching people lately. (Although I do wonder if it counts backlinks from one of my articles to another as a comment.)

The mathematics blog starts the month at 22,837 total views, and with 454 WordPress followers.

The most popular articles in March, though, were the set you might have guessed without actually reading things around here:

I admit I thought the “how interesting is a basketball tournament?” thing would be more popular, but it’s hampered by having started out in the middle of the month. I might want to start looking at the most popular articles of the past 30 days in the middle of the month too.

The countries sending me the greatest number of readers were the usual set: the United States at 658 in first place, and Canada in second at 66. The United Kingdom was a strong third at 57, and Austria in fourth place at 30.

Sending me a single reader each were Belgium, Ecuador, Israel, Japan, Lebanon, Mexico, Nepal, Norway, Portugal, Romania, Samoa, Saudi Arabia, Slovakia, Thailand, the United Arab Emirates, Uruguay, and Venezuela. The repeats from February were Japan, Mexico, Romania, and Venezuela. Japan is on a three-month streak, while Mexico has sent me a solitary reader four months in a row. India’s declined slightly in reading me, from 6 to 5. Ah well.

Among the interesting search terms were:

  • right trapezoid 5 (I loved this anime as a kid)
  • a short comic strip on reminding people on how to order decimals correctly (I hope they found what they were looking for)
  • are there other ways to draw a trapezoid (try with food dye on the back of your pet rabbit!)
  • motto of ideal gas (veni vidi v = nRT/P ?)
  • rectangular states (the majority of United States states are pretty rectangular, when you get down to it)
  • what is the definition of rerun (I don’t think this has come up before)
  • what are the chances of consecutive friday the 13th’s in a year (I make it out at 3/28, or a touch under 11 percent; anyone have another opinion?)

Well, with luck, I should have a fresh comic strips post soon and some more writing in the curious mix between information theory and college basketball.

How My Mathematics Blog Was Read, For January 2015


And after reaching 20,000 views on the final day of December, 2014, could I reach 21,000 views by the end of January? Probably I could have, but in point of fact I did not. I am not complaining, though: I finished the month with 20,956 page views all told, after a record 944 pages got viewed by somebody, somewhere, for some reason. This is a record high for me, going well past the 831 that had been the January 2013 and December 2014 (tied) record. And likely I’ll reach 21,000 in the next couple days anyway.

According to WordPress, this was read by 438 distinct visitors, reading 2.16 views per visitor on average. That isn’t quite a record: January 2013 remains my high count for visitors, at 473, but it’s still, all told, some pretty nice numbers especially considering I don’t think I had my best month of blog-writing. I can’t wait to get some interesting new topics in here for February and see that they interest absolutely nobody.

The new WordPress statistics page is still awful, don’t get me wrong, but it has been getting a little bit better, and it does offer some new data I couldn’t gather easily before. Among them: that in January 205 I received 197 likes overall — a high for the past twelvemonth, which is as far as I can figure out how to get it, and up from 128 in December — and 51 comments, up from December 29, and also a high for the twelvemonth.

The three countries sending me viewers were, once again, the big three of the United States (594), Canada (56), and the United Kingdom (52), with Austria sending in 32 viewers, and Germany and Argentina ending 22 each. And India, for a wonder sent me a noticeable-to-me 18 readers, although on a per capita basis that still isn’t very many, I admit.

There was a bumper crop of single-reader countries, though, up from last month’s six: Belgium, Estonia, Finland, Greece, Hungary, Indonesia, Iraq, Japan, Kuwait, Libya, Mexico, Paraguay, Slovakia, and the United Arab Emirates each found only one person viewing anything around here. Greece and Mexico are repeats from December.

This month’s most popular articles were mostly comic strip posts, although they were a pretty popular set; none of these had fewer than 35 views per, which feels high to me. The top posts of the last 30 days, then, were:

  1. Reading the Comics, January 6, 2015: First of the Year Edition, in which I included drawing a sloppy `2′ as a snoring `Z’ as somehow connected to mathematics.
  2. Reading the Comics, January 24, 2015: Many, But Not Complicated Edition, which includes an explanation for why margins of errors on surveys are always like three or four percent.
  3. Reading the Comics, January 11, 2015: Standard Genres And Bloom County Edition, in which I reveal my best guess for Jon Bon Jovi’s shorts size in the late 80s.
  4. 20,000: My Math Blog’s Statistics, because my narcissism is apparently quite popular?
  5. Reading the Comics, January 17, 2015: Finding Your Place Edition, where, again, I can flog that thing about a watch as a compass.
  6. How Many Trapezoids I Can Draw, which also reveals how many trapeziums I think are different in interesting ways.
  7. A bit more about Thomas Hobbes, and his attempt to redefine the very nature of mathematics, which didn’t succeed in quite the way he wanted.

Among the interesting search terms that brought people here the past month have been ([sic] on all of them):

  • science fiction and trapazoids (Somebody should totally write the definitive SFnal treatment of trapezoids, I agree.)
  • food. stotagre nebus (I feel strangely threatened by this.)
  • a group of student offer at least one of mathematics,physics, and statistcs , 14 of them offer mathematics, 12 offer physics,and 16 offer statistics.7 offer statistics and maths 6 offer maths and physics, 4 offer physics and statistics only, while 5 offer all the three subject (Help?)
  • hiw to draw diffrent trameziums
  • soglow otto radio (Pretty sure I used to listen to that back on WRSU in my undergrad days.)
  • if a calendar has two consecutive months with friday the 13th which would they be (February and March, in a non-bissextile — that is, non-leap — year)
  • how to measure a christmas tree made of triangles and trapeziums (I would use a tape measure, myself)

So if I would summarize January 2015 in my readership here, I would say: tramezium?