Subj : Re: Hey Nick To : alt.tv.farscape From : Jim Larson Date : Tue Sep 06 2005 02:26:46 From Newsgroup: alt.tv.farscape weirdwolf wrote: > Jim Larson wrote in > news:Xns96C85DFBB4CE3v234oiwofui3284af93@130.133.1.18: > >> weirdwolf wrote: >> >>> Jim Larson wrote in >>> news:Xns96C7DDDCD78E23v234oiwofui3284af93@130.133.1.18: >>> >>>> weirdwolf wrote: >>>> >>>>> Jim Larson wrote in >>>>> news:Xns96C7D1AFD4DF83v234oiwofui3284af93@130.133.1.18: >>>>> >>>>>> weirdwolf wrote: >>>>>> >>>>>>> You know you were saying about how you would trust a big U.S. >>>>>>> news corporation to give the facts correctly: >>>>>>> >>>>>>> http://makeashorterlink.com/?K2F412CBB >>>>>>> >>>>>> >>>>>> (All the cool kids use tinyurl.com) >>>>>> >>>>> >>>>> Well there's the problem, I'm all hot and sweaty. >>>>> I did however show some adults today the thing about the internal >>>>> angles >>>>> in a triangle don't add up to 180 degrees and pi isn't 3 an a bit >>>>> that I >>>> >>>> (Sphere? Poincare plane? What?) >>> >>> Balloon. You draw a triangle on a ballon and then inflate it. You >>> then put it ontop of something circular like a mug and push the >>> centre part down. I've found that it's the best way to get people >>> thniking about it, cheap and simple to do as well. >>> >> >> (Positive curvature then. Kind of impossible to demonstrate the >> hyperbolic case with real props.) > > We have several buildings in my area with hyperbolic paraboloid shaped > roofs. They are rather nifty. Of course it's not that uncommon a shape, > think a power station cooling tower cut vertically down the centre. > They were all designed by a local architect called Sam Scorer. > Not a great picture I'm afraid but the best I could find: > http://www.lincoln.ac.uk/home/newsbyte/issue10-img/scorer-library.jpg > Yes, yes, but that's not quite as easy to produce as something with obviously positive curvature (with props and stuff) like say, a sphere. Also, it's not really the negative curvature analogue to a sphere, since that has constant positive Gaussian curvature at every point. The canonical hyperbolic paraboloid has asymptotically 0 curvature in any direction away from the origin. An analogue with constant negative curvature is generally difficult to picture in R^3. You could take something like a pseudosphere (surface of revolution of a tractrix) or Kuen's surface, which just looks freaky. But again, not exactly easy prop material. > You should have seen the puzzled look on my face when I was reading a > book on n dimensional geomotry where n was greater than 3. Hell I get > confused reading Euclid, but it's a lot more interesting than just > counting things when you look at the patterns and weird stuff. > Woohooo! (I spent a number of years in a PhD program in math before switching to CS. My area of research was CAT(0) spaces, which are a type of negatively curved length space, but not in the traditional sense, since they are not necessarily anywhere differentiable. They are defined largely in terms of how triangles behave on them...which is a lot like what you were trying to demonstrate to your amazed audience. Barbie says, "Math is cool!") ((P.S. I've forgotten so much, it's like someone took several years of my life and fluhed it down the proverbial crapper. Also, you get so immersed in technical minutiae so fast, that fun examples totally elude you. Sort of like walking up to a radio astronomer and asking him of where in the sky to look for Sirius and getting the response, "Huh?")) -- Jim .