Khan Academy has released a new library to typeset mathematical notation on webpages, called KaTeX.
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- Imagine you have some playing cards. Of course if you actually have some cards you don’t need to imagine!
- Pick your favourite natural number $n$ and put a deck of $n$ cards in front of you. Then repeat the next step until the deck is empty.
- Take $2$ cards from the top of the deck and throw them away, or just take $1$ card from the top and throw it away. The choice is yours.
Have fun playing with curvature
Recently Tim Hutton and Adam Goucher have been playing around with hyperbolic tesselations. That has produced a {4,3,5} honeycomb grid for the reaction-diffusion simulator Ready, which Adam talked about on his blog a couple of days ago. Tim has also made a much simpler toy to play with in your browser: a visualisation of mirror tilings (the Wythoff construction) in spaces with different curvatures.
Hyperplay lets you select the kind of regular polygon you want to tile, and then your mouse controls the curvature of the space it sits in. Certain curvatures produce exact tilings of the space – for example, triangles tile a space with zero curvature – and you get projections of polyhedra for certain positive curvatures.
Discovering integer sequences by dealing cards
Let’s play a game:
If you pick a small $n$, such as $n=3$, it’s pretty easy to see how this game is going to play out. Choosing to throw away $2$ cards the first time means you’re then forced to throw away $1$ card the next time, but only throwing away $1$ card the first time leaves you with a choice of what to throw away the next time. So for $n=3$ there are exactly $3$ different ways to play the game: throw $2$ then $1$, throw $1$ then $2$, or throw $1$ then $1$ then $1$.
Now, here comes the big question. How does the number of different ways to play this game depend on the size of the starting deck? Or in other words, what integer sequence $a_0$, $a_1$, $a_2$, $a_3$, $a_4$, … do we get if $a_n$ represents the number of different ways to play the game with a deck of $n$ cards? (We already know that $a_3=3$.)
James Grime’s house-building problem
Aperiodipal James Grime has put a new video on his YouTube channel. He’s got a problem to do with building houses:
But James posts fantastic videos about maths puzzles all the time; what’s so notable about this one?
I was involved, that’s what! The puzzle can be done on pen and paper but it involves a lot of drawing and calculating, so James asked if anyone could make a computery version. I spent my day off work last week making just such a thing: the computerised Building Houses Problem.
Dark days for MathML support in browsers
For a brief moment at the start of the year, Google’s Chrome browser could render mathematical notation written in MathML. Since then, things have got worse for mathematics on the web.
In February, the MathML rendering code was removed by Google, citing concerns about security and code quality. Now, a member of the Chromium team has announced that Google will not be supporting MathML in the foreseeable future:
MathML is not something that we want at this time. We believe the needs of MathML can be sufficiently met by libraries like MathJax and doesn’t need to be more directly supported by the platform. In areas where libraries like MathJax are not good enough, we’d love to hear feedback about what APIs we would need to expose so that MathJax, et al, can create an awesome MathML implementation.
Peter Krautzberger, manager of the MathJax project, is not happy.
The arXiv has enabled MathJax!
A bit of slightly overdue but welcome news: the arXiv has enabled MathJax on paper abstract pages. Authors have regularly been using LaTeX syntax in their titles and abstracts, but now the arXiv typesets them automatically for you.
Chrome no longer supports MathML
Recently we reported that Chrome has added support for MathML, a good method for representing maths on the web. Now a comment on a discussion about enabling MathML in Chromium, the open source web browser project from which Google Chrome draws its source code, has announced that this feature will be turned off, for now. The comment, from user meh@chromium.org yesterday, says:
Note that MathML has had to be turned off because the code is not yet production ready.
We hope to turn it on in some future release. We plan to announce this in the Chrome 25 release notes.
Earlier today user isherman@chromium.org posted this clarification:
To summarize the current status of this bug: We’d like to enable MathML in Chrome, but the WebKit code still needs further improvements before we can ship it.
Further information: Enabling support for MathML.