Subj : Re: Hey Nick To : alt.tv.farscape From : Nick Date : Tue Sep 06 2005 02:31:43 From Newsgroup: alt.tv.farscape Jim Larson wrote: > 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?")) > .