by PWrong » Fri Aug 06, 2004 3:50 pm
That's what I thought at first, but you can't wrap a point around a square either. Then again, I suppose you could wrap a 0-sphere (which is just two points) around a square, but not a cube.
The 2D analogue of a 1-D coil wrapped around a cube would be a square with two sides covered in points. It seems like you wouldn't be able to cover 4 of the 6 faces of a cube with a 0-D coil, without changing the radius.
It all depends on what you mean by "wrap", of course. If a line can't wrap around an object, what can it do?
For an axle of any dimension, and a string, or 1-sphere, of arbitrary length. I'll suggest that the following is true. I'm not sure, someone can tell me if I'm wrong. You can put a large circle in the string, put the axle through the circle, and then tighten the knot. Then with the string left over, you make another circle, and do it again. And so on. The problem is you can only cover 4 sides/faces/cells in this manner. So you can wrap a square entirely, or wrap a cube with the front and back faces remaining, or wrap a tetracube with the front, back, apos and zapos cells remaining.
Unfortunately, that kind of wrapping won't produce the same magnetic field as a 4D magnet. Maybe electricity should move through planes. But if you wrapped a planar wire around a flunar axle, would the electricity generate the correct magnetic field?
I haven't looked at the geometry forum much, but it seems like problems like this can only really be solved using vectors and maths notation, since we can't actually visualise the objects.