A video about the Mobius strip, with an interesting choice of background music.
This video illustrates certain classical facts about the Mobius strip:
- if you draw a line down the middle of the Mobius strip, it runs down "both sides" of it (by which I mean both sides of the original sheet of paper; the Mobius strip isn't orientable)
- if you cut along that line, you end up with a long twisted strip;
- if you cut along a line one-third of the way from one of the edges of the original strip of paper to the other, you get two linked strips, of equal thickness but different lengths;
and another fact I didn't know:
- if you cut along a line one-quarter of the way from one of the original edges to the other, you get three linked strips (I assume at least one of them is Mobius), but now one is twice as wide as the other two. (But I think there's something trickier going on with the cutting here; it's hard to get a good look.)
Also, breaking the underwater one-handed Rubik's-cube-solving record. I can't make this stuff up.
(These are both from is from sciencehack, which is a site for science videos that claims that "every science video on ScienceHack is screened by a scientist to verify its accuracy and quality". Apparently they don't host the videos; they just index other people's science-related videos.) Here is their index of mathematics videos.0