Monday, September 12, 2005

Day 132

Today's DIY attempts got me thinking about differential geometry.

One of the things about living in an oldish house is that nothing is quite square or quite straight. As I was trying to fix new skirting boards to the walls in the kitchen, this became increasingly clear. If one end was flush with the corner, the other end was an inch above the floor, and vice versa. Not content with one axis of distortion, the wall is also (of course) not straight, so the skirting board had to bend along its length (which is at least possible— I had to just pick a compromise position for the first axis of distortion).

So I guess something that looks straight to the naive observer but which is actually curved in two different directions would have some number of non-zero components for its Riemann curvature tensor. And to be honest, I'm not sure there wasn't some torsion in there too.

Of course, the actual attachment of the skirting boards was made more difficult by the fact that the masonry nails I was trying to use wouldn't go into the wall. I was hitting them pretty hard with the hammer, but they just stopped after a bit, then gave out sparks and bent rather than sinking deeper into the wall. In the end, I had to just glue the skirting boards to the wall, and use the partially-sunk nails and some jerry-rigged contraptions to press them against the walll while the glue dries.

Tiling the fireplace moved from an affine connection to a metric, with 15x15 cm tiles acting as a suitable coordinate patch. One direction was reasonably flat (thanks to some earlier efforts), but the other two directions only looked rectangular. Still, at least I now have the tool of choice for adjusting the metric, even if non-square cuts have to be done freehand (at risk of dedigitizing). Reg also decided to assist again but since tile glue is less permanent than paint, I just ignored the pawprints.

[A:12056 B:155 C:0 D:9187 Total:21398]

1 comment:

Matt said...

man.. if it reminds you of differential geometry you shouldn't do it. I stopped studying differential geometry for similar reasons