Re: Is it permitted in math to go beyond?

Hero wrote:

(what I wrote before)
Now this is all embedded in the Euclidean plane...

My bad. To think of it the way you wish to, embed it in the real projective
plane. The points at infinity are then included in the ultra-ideal points.

In the Klein disk, you could have two lines that are segments of Euclidean
lines that are parallel.


Or the same expressed differently: In the Klein-disc two straight
lines are hyper-parallel, when these lines prolonged through the edge
of the disc interect outside in an ultra-ideal point.
From Klein to Poincare i have to do parallel projection onto half of a
sphere, followed by stereographic projection onto a plane. Already
with the first projection i'm stuck: whereto these ultra-ideal points
move?

While convenient, I think there might be a better way to transform the Klein
disk into the Poincare disk that carries the whole plane along -- that's
your problem in the first projection. I know I've read this somewhere,
maybe in Coxeter? Let me see what I can find.

--charlie
.

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