The magic number 25641

Reader of the site Bhaskar Hari Phadke has written in to tell us this fun fact about the number $25641$. It’s easier to show than to describe, so here goes:

25641 \times \color{blue}{1} \times 4 &= \color{blue}{1}02564 \\
25641 \times \color{blue}{2} \times 4 &= \color{blue}{2}05128 \\
25641 \times \color{blue}{3} \times 4 &= \color{blue}{3}07692 \\
25641 \times \color{blue}{4} \times 4 &= \color{blue}{4}10256 \\
25641 \times \color{blue}{5} \times 4 &= \color{blue}{5}12820 \\
25641 \times \color{blue}{6} \times 4 &= \color{blue}{6}15384 \\
25641 \times \color{blue}{7} \times 4 &= \color{blue}{7}17948 \\
25641 \times \color{blue}{8} \times 4 &= \color{blue}{8}20512 \\
25641 \times \color{blue}{9} \times 4 &= \color{blue}{9}23076

A good one to challenge a young person with.

I did a little bit of Sloanewhacking and found a couple of sequences containing $25641$ which almost, but don’t quite, describe this property. So, semi-spoiler warning: you might enjoy A256005 and A218857. I’d like to come up with the ‘magic number’ which looks the least like it’ll have this property – any ideas?

Thanks, Bhaskar!

“π – It’s Complicated” – a talk I gave on Pi Day 2016 at Ustinov College Café Scientifique

I was invited to give a talk for Ustinov College’s Café Scientifique on π Day this year. The turnout wasn’t great and I put quite a bit of effort into the slides, so I wanted to put it online. I’ve finally got hold of the recording, so here it is. Unfortunately they didn’t set the camera’s exposure properly, making the screen illegible, so you’ll probably want to follow along with the slides in another window.

I tried to come up with a way of writing today’s date as a multiple of π Day, but couldn’t make it work. However, I did realise that Halloween (31/10) is the best approximation to π between now and the next π day (I think). Sπooky!

Best way to explain topology: now officially ‘using baked goods’

Nobel Prize news!

The 2016 Nobel Prize in Physics has been awarded to a trio of physicists: Michael Kosterlitz, Duncan Haldane and David Thouless“for theoretical discoveries of topological phase transitions and topological phases of matter”.

And here’s the maths angle – their work is in the field of topological physics, which relates strange matter (superconductors, superfluids and the like) to topology, via the interesting way the properties of the materials change in phases, like the different fundamental shapes of objects in topology. None of the material we’ve taken a cursory glance at so far yields a simple explanation of how these two things are linked, but they have explanatory PDFs on the Nobel website if you’d like a dig around: Popular (PDF) and Advanced (PDF).

Also, impressively many newspaper headlines seem to have failed to notice that ‘strange matter’ is actually a thing in physics, and consequently mangled it in their explanations.

Cue of course an amazing press conference in which Nobel Committee for Physics member Thors Hans Hansson holds up a bun, a bagel and a pretzel to explain the difference. Classic topology.

More information

Official Nobel press release

British scientists win Nobel prize in physics for work so baffling it had to be described using bagels, at The Telegraph (bonus points for ‘Noble prize’ typo, if it’s not been corrected yet)

Physics prize explanations on the Nobel website: Popular (PDF) and Advanced (PDF)


The world’s smallest Rubik’s cube is 5.6mm wide and absolutely adorable

I just found this video of a very focused man showing off a teeny tiny Rubik’s cube. It’s 5.6mm on each side, which apparently makes it the smallest in the world, beating some relatively gigantesque efforts of 6mm and larger.

Watch this video; I’ll warn you now that the squee factor gives way to some very dry detail quite quickly.

The cube was made by Tony Fisher, by filing down a 3D-printed 6mm cube. I hadn’t heard of Tony before, which surprises me – his site is full of all sorts of incredible twisty puzzles.