Today I learned: the first English translation of Euclid included pop-ups for 3-D proofs. (I was fact checking a claim that John Dee was the translator. No, but he wrote the preface and did some editing.)

Platonic solids in bubbles!

Atmospheric Circulation of Hot Jupiters

Abstract
The full-phase infrared light curves of low-eccentricity hot Jupiters show a trend of increasing dayside-to-nightside brightness temperature difference with increasing equilibrium temperature. Here, we present a three-dimensional model that explains this relationship, in order to provide insight into the processes that control heat redistribution in tidally locked planetary atmospheres. This three-dimensional model combines predictive analytic theory for the atmospheric circulation and dayside–nightside temperature differences over a range of equilibrium temperatures, atmospheric compositions, and potential frictional drag strengths with numerical solutions of the circulation that verify this analytic theory. The theory shows that the longitudinal propagation of waves mediates dayside–nightside temperature differences in hot Jupiter atmospheres, analogous to the wave adjustment mechanism that regulates the thermal structure in Earth's tropics.

Happy New Year!

Byrne's edition of Euclid's Elements, online.

ht: Open Culture

So, they're teaching 'Africentric maths' up North. I've not much comment on the article per se, but I did want to mention that a) it's not a bad idea because b) the Egyptians had some brilliant, bizarre things going on even if c) the school in question (at least from this article) is just doing math with some pyramids thrown in.*

But in truth Egyptian math is a wonderful example of practical restrictions leading to deep understanding. Let's look at their use of fractions:

Time sink of the week: Cut the Knot.

A new class of regular polyhedra?

Trashy action movie director to make ass-kicking film about Sir Isaac Newton.

Counting to five-ish.

Collaborative math via blogs, plus Tic Tac Toe in four dimensions.

Happy Ada Lovelace day. In honor of this iteration, I wrote some code today--which actually compiled. I mark this day with a white stone, indeed.

Humans worsted by pigeons at the Monty Hall problem

In the experiments, the birds quickly reached the best strategy for the Monty Hall problem — going from switching roughly 36 percent of the time on day one to some 96 percent of the time on day 30.

On the other hand, 12 undergraduate student volunteers failed to adopt the best strategy with a similar apparatus, even after 200 trials of practice each.

"In additional to the intellectual stimulation, you get more cream cheese, because there is slightly more surface area."

How to cut a bagel into linked halves.

Edit: Also, "Mobius Lox" would be a great name for a band.

And further semi-nosferatic news: the horseshoe bat's nose, explained.

Much like a flashlight with an adjuster that can create an intense but small beam of light, the bat's nose can create a small but intense sonar beam. Mueller and his team used computer animation to compare varying sizes of bat noses, from small noses on other bats to the large nose of the paradoxolophus bat. In what Mueller calls a perfect mark of evolution, he says his computer modeling shows the length of the paradoxolophus bat's nose stops at the exact point the sonar beam's focal point would become ineffective.

Man, math's great when it works.

Very well, here: Euclid 1.47, the musical version, in Swedish.

Mrs. P comments, "Oh, so that's how you seduce an old, Swedish mathemetician." Yup. Myself, I'd give substantial quantities of alcohol for a witty, singable translation.

Courtesy of John Derbyshire.

Also, in the spirit of the season: Pascha explained. Apologies in advance; blame this guy.

John Derbyshire has had better things to do than follow politics of late. Politics' loss is very much our gain. He and Odious seem to court the same muse.

Sketch of
The Analytical Engine
Invented by Charles Babbage
By L. F. MENABREA
of Turin, Officer of the Military Engineers
from the Bibliothèque Universelle de Genève, October, 1842, No. 82

With notes upon the Memoir by the Translator
ADA AUGUSTA, COUNTESS OF LOVELACE

...is well worth your time, if you are the sort of person who said to themselves, 'Ooo! Analytical engine!' when you read that. (ht)

From Not To Go on Four Legs:

INTERVIEWER: So what is it like to spend years of your life working on a mathematical problem of this magnitude?

PROF. BARRA: My students have asked me that, and I have a rather elaborate metaphor, if you don't mind. It's like a dream in which you go to climb a rock pinnace. You can't see the top of it, and while you can plan your ascent from the bottom to some degree--I'll put my hand there and my foot there, and then I'll be able to reach there, and so forth--you can't really know how you can climb until you begin. And of course you don't really know what's at the top.

I: But you have an inkling.

B: Yes. You know something of the shape of the rock, and something about how you're going to climb it, and something about what you'll find at the top. But not very much! And as you climb, you can spend as much time examining each hand hold as you like. In fact, since it's a dream you have that peculiar ability to focus on one object to the exclusion of everything else, and you can see every detail perfectly. That object can become your whole world, and it's easy to forget about the rest of the climb.

I: What about the climb?

B: Well, if you can keep a memory of where you're headed, you just keep finding these holds. They can be as tenuous as you want, as long as they'll support you. It's just a question of finding a new hold and moving a little bit further every time. Of course you can get stuck!

I: And then what?

B: Well, you can try to climb down a bit and find a new path. Or you can try to carve out a hand hold. But sometimes you fall. Of course the only thing that happens if you fall is that you wake up. Nobody has ever died of an unproved theorem.* But I'm sure you know how hard it can be get back to a dream after you've awoken....

*Does Archimedes count, do you think? μή μου τούς κύκλους τάραττε and all that.

Islamic decoration and quasicrystal patterns: a very interesting piece on NPR tonight related how Islamic decorative patterns from the 14th C. and earlier hit upon modern mathematical concepts called quasicrystal patterns (see also aperiodic tiling), which I don't pretend to understand. Here is an article with much more on the mathematical and artistic aspects. Here is how to produce such patterns with lasers.