• OMICS Group now charging for article withdrawals (\(\mathbb{M}\)): a new way for predatory journals to be predatory. It’s probably even legal: they have begun providing you with a service (reviewing of your paper) and told you up front what the charges are. Whether it’s ethical for scientific publishing is an entirely different question… So let this be a lesson to be careful where you submit, because unsubmitting could be difficult.

  • Sunset geometry (\(\mathbb{M}\), via). How to tell the radius of the earth from a photo of a sunset over a still body of water (knowing the height of the camera over the water). Not explained: how still the water needs to be, how badly the results are affected by atmospheric refraction, how accurately the measurements need to be performed to get a meaningful estimate, or how likely you are to see the sun meet the horizon before low clouds get in the way.

  • The new AMS fellows (\(\mathbb{M}\)) include graph theorists Daniel Kráľ and Bojan Mohar, and fellow Wikipedia editor Marie Vitulli. Their announcement also led me to create new Wikipedia articles on new fellows Chikako Mese, Julianna Tymoczko, and Jang-Mei Wu, and Vitulli to create one for Tara Brendle. Congratulations, all!

  • The graph menagerie: abstract algebra and the mad veterinarian (\(\mathbb{M}\)). Or, how to solve puzzles like: “Suppose a mad veterinarian creates a transmogrifier that can convert one cat into two dogs and five mice, or one dog into three cats and three mice, or a mouse into a cat and a dog. It can also do each of these operations in reverse. Can it, through any sequence of operations, convert two cats into a pack of dogs? How about one cat?”

  • LIPIcs series editor Luca Aceto polls the community on page limits (\(\mathbb{M}\)). It used to be that conferences in theoretical computer science had page limits because you couldn’t bind volumes with too many paper pages, now long irrelevant. So now that we can publish much longer conference papers, should we? Limits encourage authors to publish full details in a properly refereed journal version, but unlimited length recognizes the reality that many authors are too lazy to make journal versions.

  • Squaring the square, in stained glass (\(\mathbb{M}\), via). By David Spiegelhalter, 2013.

  • Tiling the plane by edge reflection (\(\mathbb{M}\)). Here’s a proof sketch that there are eight ways to do this: Each prototile vertex must have angle \(2\pi/i\) for integer \(i\), and if \(i\) is odd, the subsequence of the remaining angles must be symmetric. For an \(n\)-gon, considering the sum of interior angles shows that

    \[\sum\frac{1}{i} = \frac{n-2}{n}.\]

    Searching for sequences of integers with these properties (choosing the smallest integers first to make the search bounded) finds that the only cyclic sequences of integers meeting these constraints are (3,12,12), (4,8,8), (4,6,12), (6,6,6), (3,4,6,4), (3,6,3,6), (4,4,4,4), and (3,3,3,3,3,3), the sequences of the 8 known tessellations.

  • Turkish academics sound alarm over gender segregation plans (\(\mathbb{M}\)). When women’s universities are set up to provide alternatives in the face of persistent discrimination against women in the existing universities (as they were in the US and Korea), that’s one thing. When the women are already successful in the existing universities but women’s universities are set up as a pathway to push them out, that’s entirely different.

  • Engineers put Leonardo da Vinci’s bridge design to the test: proposed bridge would have been the world’s longest at the time; new analysis shows it would have worked (\(\mathbb{M}\), via). I don’t think the link does justice to the scale of the thing. Da Vinci proposed a single stone arch across the Golden Horn in Istanbul, roughly 280m. That’s much longer than anything on the current list of the world’s biggest stone arches.

  • Order polytope (\(\mathbb{M}\)). New Wikipedia article on a convex polytope derived from any finite partial order as the points in a unit hypercube whose coordinate order is consistent with the partial order. Its vertices come from upper sets, its faces come from quotients, its facets come from covering pairs, and its volume comes from the number of linear extensions of the partial order. Coordinatewise min and max gives its points the structure of a continuous distributive lattice.

  • Socked into the puppet-hole on Wikipedia (\(\mathbb{M}\)). Journalist Noam Cohen’s Wikipedia biography is collateral damage in the war on slowking4, a prolific creator of Wikipedia articles whose problematic behavior (copying content from other sites, creating sockpuppet accounts to hide their identity, and reinstating articles from another user that were so riddled with errors that they were deleted en masse) has led to delete-on-sight actions.

  • Arithmetic billiards (\(\mathbb{M}\)): using billiard ball trajectories to compute number-theoretic functions.

  • olligober made a regex to match all multiples of 7, but it was more than 10,000 characters long so grep couldn’t handle it. Applying Kleene’s algorithm to convert the natural DFA for this sort of problem into a regular expression blows its size up from polynomial in the modulus to exponential, but is this necessary? And if it is, what is the best possible base for the exponential?

  • Dividing a chocolate bar into any proportions (\(\mathbb{M}\)). The bar has \(L\) squares, and you want to give each of \(m\) people an integer number of squares, but the integers are not known in advance. How to break the bar into few pieces so this will always be possible? Reid Hardison asked this months ago but Ilya Bogdanov answered with an efficient construction of the optimal partition much more recently.

  • Geometry and Billiards (\(\mathbb{M}\)). An undergraduate-level textbook on the mathematics of reflection by Serge Tabachnikov.