Hyberbolic Plane, Negative Curvature 3:4

[purplecat]

This is basically the same as my last crochet effort, except a bit frillier, but I was experimenting with the knit-purl version of crotcheting.







This entry was originally posted at http://purplecat.dreamwidth.org/27876.html.

Comments

[purplecat]

`hyperbolic plane' is a fancy name for a frill. Playing with lines on hyperbolic planes gets a bit technical but just what one is, is a frill.

[lukadreaming.livejournal.com]

*Squirrels latest bit of info away*

How do they relate, then, to the lines that don't meet? (And explain next time you see me if that's easier!)

[purplecat]

Well if you draw two "straight" lines on a hyperbolic plane which don't meet, they don't stay a uniform distance apart like "sensible" straight lines ought to.

I've put "straight" in quotes because they are straight lines as far as the frilly surface is concerned but you'd look at them and say "these lines are obviously curves". I'm trying to crotchet up a fairly large plane for you and then I'll put some "straight" lines on it and try to explain a bit better - like why I feel justified in asserting that the frill thinks an obviously curved line is straight.

[lukadreaming.livejournal.com]

Got it. I think *g*.