# You're reading: Posts Tagged: maths on the web

### Discovering integer sequences by dealing cards

Let’s play a game:

1. Imagine you have some playing cards. Of course if you actually have some cards you don’t need to imagine!
2. 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.
3. 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.

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:

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.

### Chrome now supports MathML

Update 07/02/2013: Google giveth, and it taketh away. MathML support in Chrome has been disabled until it’s “production-ready”.

Putting maths on the web has always been a tricky proposition. Typesetting notation is a highly complicated procedure, so for years people have got by either by compromising on aesthetics and writing equations in plain, unadorned text, or by using off-line LaTeX compilers to make blurry images of what they’re trying to say.

### Factor Conga

Quite a few designery visualisations of the prime numbers have been put out on the web recently, to varying degrees of success. Most of the time they look pretty but don’t tell you very much; the most recent example I can think of is El Patrón de los Números Primos by Jason Davies.

A few weeks ago Brent Yorgey posted on his excellent blog The Math Less Traveled some really nice “factorization diagrams“, along with the code to produce them. Straight away, anyone with a text editor and a knack for fancy web coding set to work making the animated version that was so clearly required.

Stephen von Worley has made, I think, the nicest one. He calls it the Factor Conga. Sit back and enjoy the mysteries of the natural numbers as they dance their beguiling dance!