As promised, another picture of my geeky craft projects. The green, orange and red parts of this string are made from one strand of yarn, the blue parts I made separately and added later.
The blue things are, left to right, a tetrahedron (shape with four (more-or-less) regular triangular sides), a spiraling tube, a square donut, a box with six edges, a cube, and a not quite spherical sphere.
The two orange things in the middle are Moebius strips. If you follow one side of the strip, or the edge, you’ll find that it has only one side, and only one edge. Or that is the way it was explained to me, when I learned about them at first. But when crocheting a Moebius strip I found that that is actually not true: it does have two sides, but the front and the back of the strip are next to each other. There is, however, just one edge.
The little green ‘knot’ on the far left of the picture is also a Moebius strip, but one where the edge is shorter than the middle. Every next line of stitches I skipped every third sticht or so. It quickly becomes impossible to go on, as the edge gets too small to get around. I did the opposite to the first of the orange Moebius strips: every next line I added a few stitches, which gives it its flare.
Later I realised that this flared Moebius strip is an example of a surface with ‘negative curvature’: the surface curves away from you in one direction, and towards you in another. The science news piece on ‘crafty geometry’ features a hyperbolic plane, which has the same curvature on every point (I’m not sure if that’s the case in the flared moebius). It’s called hyperbolic because you need hyperbolic geometry to describe the way lines on a plane like that behave. I made a bigger model of a plane like that too, out of little triangles, but I haven’t got a photo of it yet. When I have, maybe I’ll write yet another post…