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From: Nicolas George <nicolas$george@salle-s.org>
Subject: Re: request please for an ascii drawing of a saddle and a huge ball
 that would fit into the saddle; for math
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Date: 17 Jan 2007 16:13:30 GMT
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Faux_Pseudo  wrote in message <iQqrh.57582$kn7.27307@newsfe23.lga>:
>> This is a ascii art for math and sci.math. Can someone please draw a
>> saddle and then draw a huge ball that
>> would sit on top of the saddle as to ride the saddle. The idea is that
>> the ball is Riem geom and the saddleshape
>> is Lobachevskian geom.
> 
> What is a lobachevskian geom?
> http://en.wikipedia.org/wiki/Hyperbolic_geometry
> Or a Reim geom?
> http://images.google.com/images?q=Riemannian%20geometry

He probably means respectively hyperbolic and parabolic.

I hate it when people use the name of someone instead of a meaningful name
to designate a mathematical object.

> How big did you want this thing?  This big?
>               __
>              (  )
>               \/     _
>              / \`---' \
>             /_.-\_.--._\
> 

I believe he wants something like that (sorry, this is not really ASCII-art;
but this is too hard for me):

camera { location <0.5, 0.5, -2> look_at <0, 0.1, 0> }
light_source { <10, 10, -20> rgb <2, 2, 2> }
quadric { <-1, 0, 1>, 0, <0, 1, 0>, 0
  clipped_by { box { <-0.7, -10, -0.7>, <0.7, 10, 0.7> } }
  pigment { rgb <1, 0, 0> }
  finish { ambient 0.2 specular 1 }
}
sphere { <0, 0.5, 0>, 0.5
  pigment { rgb <0, 1, 1> }
  finish { ambient 0.2 specular 1 }
}

The sphere has to be in the bottom of the saddle, and be as big as possible
to fit in the ridge. It is called the osculating sphere at this point.