"What's that interest mean?" meme

[pne]

1. Scan my interest list and pick out the one that seems the most odd to you.
2. I'll explain it.
3. Then you post this in your journal so other people can ask you about your interests.

Comments

Klein bottle

[pne.livejournal.com]

Ooh... complicated.

Lessee. Do you know what a Möbius strip (http://en.wikipedia.org/wiki/M%F6bius_strip) is? Take a longish (much longer than wide) rectangular strip of paper and bring its ends together; then twist one end 180° (a half-turn) and glue the two ends together. The resulting strip has only one side, even though the original paper strip had two sides! (Try colouring one side of the Möbius strip, for example.) Also, cutting the Möbius strip down the middle doesn't cause it to fall apart.

A Klein bottle is kind of the same thing in 3D. Only, just like you need three dimensions to make a 2D Möbius strip, you really need four dimensions to see a proper Klein bottle, but you can see approximations -- see, for example, this site (http://www.kleinbottle.com/), which sells "immersions" of Klein bottles into 3D space, out of glass. Klein bottles have no inside or outside.

See also the Wikipedia article (http://en.wikipedia.org/wiki/Klein_bottle) or the Mathworld article (http://mathworld.wolfram.com/KleinBottle.html), though both are extremely mathy.

Re: Klein bottle

[lexabear.livejournal.com]

Hmm, I remember reading some fantasy novel where they trapped a genie in one -- perhaps that's why it seemed familiar. It's an interesting concept, anyway, as with all the crazy semi-imaginary non-Euclidean theoretical stuff math can come up with.