Ben North's blog

While looking through some past and sample papers to help with some volunteer maths tutoring I do, I came across what I was fairly convinced were errors in a question in a sample paper written by the State Examination Commission. What followed was a very positive exchange of correspondence with the examiner, and the end result is that they are going to review the question. It was refreshing to have such an exchange with a public body, in particular with somebody who directly and properly engaged with my query. If only all interactions with public bodies were as satisfactory. The question The question at issue is Question 1 on paper 2 of their 2012 sample. It reads, in relevant part, The

I recently came across a post on the Makezine blog showing a video of a very pleasing mechanism, the MacDowall single-pin escapement. Zach and I recreated it as best we could, although we didn’t go as good a job as the original when it came to a rigid support structure. Nevertheless, our copy worked: My other aim with this was to experiment with temporal aliasing, to create a slow-motion version of the mechanism. For this to work, I would make a video by taking, say, every 61st frame of the original video. Since the pendulum’s period is very unlikely to be an exact multiple of the frame time, I would get a strobe effect and see the mechanism in slow

About thirty years ago, my dad and I wrote a game for our Dragon 32 home computer. It was originally a pen and paper game for two players; in our version you played against the computer. I have tried to recreate the experience on the web. It needed a bit more room than this blog format allows, so it has its own page: Cobra: a Dragon 32 game from my past Looking back now, I realise how much time Dad put in to this project, and how much effort my parents put into encouraging my interests in general. I’m very grateful to them. Epilogue Thanks to Nick Gray, I now know that this game is a variant of the Black

My 5-year-old son is mysteriously keen on a Snakes And Ladders game we have, but there is often some discussion about what the ending rule should be. The winner is definitely the person who lands on square 100 first, but what to do if you roll a number which would take you past square 100? There are two rules we play: You win. You bounce back off the end of the board. E.g., from square 98, a roll of 6 would take you: 99, 100, 99, 98, 97, 96. Photo © Nick Fedele. CC-BY-SA-2.0 Empirically, the game takes way longer if you play the ‘bounce’ rule than if you play the ‘win’ rule. But how much longer, on average? It turns out that

Some experiments to explore the ideas used by an image projector using the Fourier transform as its underlying mechanism.

The number of ways of writing an integer as the sum of a square number and twice a triangular number is the same as the number of ways of writing it as the sum of two triangular numbers.

A stop-motion animation with a bit of a story — one friend goes to visit another friend. And also sound! Animators: Jude and Zach Voice actors: Jude and Zach Camera operator: Meg Post-production: Ben (To put it together, I used Openshot again, but found it buggy and crashy this time, and the freeze-frame effect was quite fiddly to use. I also looked at kdenlive, which was in many ways much better but its freeze-frame effect didn’t seem to work if you used a clip more than once.)

© 2008, Blender Foundation : CC BY 3.0www.bigbuckbunny.org The kids had taken a few videos which they wanted to put onto their Archos Vision 14 portable media players, but the supplied software is Windows-only and wouldn’t run successfully under Wine. The example movie on the device (Big Buck Bunny) had in its metadata a comment that it had been encoded with mencoder, so I thought there was a reasonable chance that Archos’s clunky-GUI’d software just called out to mencoder to do the actual work. Running Archos’s AVIConverter on a real Windows XP machine and watching via Process Explorer revealed that this was the case. Grabbing the command-line and trying it under Linux worked: mencoder -noodml \ input-file.avi \ -of avi -o output-file.avi

Which adjectives are most commonly paired with only a few nouns? Which nouns are most commonly paired with only a few adjectives? Combining the Google N-Gram data with a parts-of-speech database yields some answers.

For Christmas, my daughter Meg gave me a hardback book which she had made herself (with help from Bear), using one of the many on-line design-your-own-book outfits, Pixum. Pixum provides a Linux version of their book-design software, which is notable and encouraging. But I could see no obvious way of exporting to PDF, and wanted to send a soft copy to my parents. The file format used by Pixum’s software is XML, and it wasn’t too tricky to work out enough of the details to produce a reasonable facsimile in PDF, using various Python packages (ElementTree, Python Imaging Library, BeautifulSoup, tinycss, ReportLab’s Pdf Library). I was not able to get the text positioning to exactly match the original printed version,