Things about making physical stuff that I think are neat.
All facts
Fabric stretches on the diagonal
Fabric
Pull a woven fabric along its threads and it barely stretches. Pull it diagonally, on the bias, and it stretches a lot.
The threads themselves don't stretch. But the little squares between them can lean over into diamonds, so the fabric gets longer one way and narrower the other. That's why bias-cut dresses drape and cling to the body.
Seam allowance
Sewing
Every CAD model of a sewn product is wrong by about 10mm. That's seam allowance, the strip of fabric tucked inside every stitch.
CAD shows the finished shape, but the factory has to cut each flat piece bigger, with that extra strip all the way round. Most designers learn this when their first prototype comes back too small.
Thickness accommodation
Origami
Thickness accommodation is the problem of making origami work with real, thick materials. Paper folds perfectly because it's basically zero thickness, but panels like foam, wood or metal have to physically wrap around each other when they fold.
So a hinge needs extra room, roughly π times the thickness it wraps around, or the panels jam. And the room needed grows as folds stack, since later folds wrap around thicker piles.
Engineers solve this by widening gaps, offsetting hinges, tapering panel edges or splitting hinges into two, which lets thick panels fold flat the way paper does.
The toolbox for thick folds
Tapered panels Bevel the panel edges so they don't collide, like cutting a V into foam so it closes.Offset hinges Move the hinge line to the top or bottom surface instead of the middle, which changes which way it folds easily.Double hinges Split one fold into two parallel hinges with a strip between, so the strip becomes the spine of a book.Membrane hinges Panels glued to a flexible fabric layer, like most folding mats. Simple, but the fabric needs slack to wrap.