Subj : Re: Hey Nick
To   : alt.tv.farscape
From : Jim Larson
Date : Tue Sep 06 2005 02:34:41

From Newsgroup: alt.tv.farscape

Nick wrote:

> Jim Larson wrote:
> 
>> weirdwolf wrote:
>> 
>>> Jim Larson <larsonjmR.E.M.O.V.E.@gmail.com> wrote in
>>> news:Xns96C85DFBB4CE3v234oiwofui3284af93@130.133.1.18: 
>>> 
>>>> weirdwolf wrote:
>>>> 
>>>>> Jim Larson <larsonjmR.E.M.O.V.E.@gmail.com> wrote in
>>>>> news:Xns96C7DDDCD78E23v234oiwofui3284af93@130.133.1.18: 
>>>>> 
>>>>>> weirdwolf wrote:
>>>>>> 
>>>>>>> Jim Larson <larsonjmR.E.M.O.V.E.@gmail.com> 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?")) 
>> 
> 
><plonk>
> 

Woohoo!

(You know you want me.)

-- 
Jim

.