Personal Blogs

I helped a teacher rearrange her classroom today. After we'd finished we both agreed that there seemed to be more space. I pointed out that there couldn't actually be any more space, we hadn't taken anything out [and we didn't do anything 3-D]. But there was more space.

I went away for a wee ponder. The main change was that instead of ten blocks of three desks there was one big block in the shape of a square W.

Ah, borders and faces!

The original arrangement had eleven faces and ten borders. The new arrangement had only one border and two faces. Does this matter? Yes, I think that it does.

For example you want to paint a room, what do you do with the furniture? You shove it all together into the centre of the room don't you? You reduce it to a single border of the shortest possible length and the faces to two.

You don't get any more floor area but you get better connected space [not a proper term].

There's something topological about this...