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Fibonacci Grids

I uploaded this video to YouTube last week but I forgot to make a post here. It’s about a moderately interesting fact about fibonacci numbers that David Cushing told me at MathsJam. I generalised it a bit, so I’ve been meaning to write a post for The Aperiodical or do a snappy video or something like that for ages.

I finally decided last week to just sit down and record myself going through the proof, so here’s that video. I deliberately didn’t prepare beforehand, so it’s just under an hour long and contains a lot of thinking out loud.

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Converting a stream of binary digits to a stream of base $n$ digits

James Coglan asked on twitter:

Suggestions wanted: how to turn an indefinite stream of bits (01110010…) into a stream of [A-Z] where letters are evenly distributed.

— James Coglan (@jcoglan) June 11, 2012

And I don’t mean just select character codes, I mean select from an arbitrary-sized character set of any length.

— James Coglan (@jcoglan) June 11, 2012

 

So you have an infinite stream of uniform random binary digits, and want to use it to produce an infinite stream of uniform random base $n$ digits.

The obvious really easy way to do it is to find the smallest $k$ such that $2^k \geq n$, and generate numbers in the range $0 \dots 2^k-1$.

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Problems I’m currently thinking about

I’ve been in a bit of a problem-posing mood recently. Hopefully I’ll do some problem-solving soon. Here are a few questions I’ve thought of but haven’t got solutions for. I haven’t done any literature searching, so these might have been done before.

All the problems are quite computery. Maybe I’m a computer scientist, really.

Problem 1: Reordering the alphabet

What reordering of the letters of the alphabet contains the most (contiguous) English words? This is a big search space problem.  I did a little bit of tinkering in python, trying first of all to find the single word which contains the most smaller words.

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Newcastle MathsJam April 2012 Recap

April’s MathsJam was very enjoyable. We did a bit of arts and crafts, a bit of playing games, and if it had been NBA Jam instead of Maths Jam I would have been entirely on fire because I used up all my IQ points solving some very fun puzzles. Durham were still on their Easter holidays so the attendance was a modest six people. That was just enough for everyone to be doing the same thing at the same time, so we had a good time.

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Slides – “Putting maths notation online”

On Monday I gave a talk at Birmingham at a workshop titled, Using social media to engage students in mathematical sciences. I have no experience of doing that, but I was invited to talk a bit about putting maths notation online. It’s basically just a collection of links to the posts I’ve written on the subject previously, but maybe big text in small slides will be more accessible.

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Newcastle MathsJam March 2012 Recap

It’s been two months since I last wrote one of these!  March was a haze of overwork and stress for me, so I didn’t write a recap for March’s MathsJam while it was still March. Peter Rowlett, who was visiting Newcastle as part of his mission to avoid having to think up new puzzles for MathsJams by always attending different ones (and also to give a talk at the university) has kindly sent me his notes, so here’s what I’ve reconstructed:

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A little applet to make maths for screengrabbing

Paul Taylor wanted an easy way to write some maths he could take a screengrab of, for use as an icon. Before I intervened he was doing something unnatural with wikipedia, so I wrote a little applet using MathJax: “make big maths“.

Quite a few tools like this exist, using mimetex or some other CGI tool to run LaTeX on a server and produce an image file. That’s far too slow and rubbish-looking for my liking, so I made my own with MathJax.

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