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NON- EUCLIDEAN NON- DIMENSIONAL CIRCUMRADIUS ???


From
mathma at usa.net
GLN,INDIA

1)I once found a twisted or constant negative Gauss curvature surface on the
 web giving (x,y,z)==f(u,v) by mathematica example..
can you/ anyone  locate it ?
2) I want to understand from non-euclidean geometry,the geometrical meaning
 of the invariant
sin a/sin A==sin b/sin B==sin c/sin C
and
sinh a/sin A==sinh b/sin B==sinh c/sin C
To comparethis  in plane two dimensional trigonometry, this becomes
 a/sin A== b/sin B==c /sin C == 2* circum radius of a triangle with straight
 line geodesics.
What is this invariant in non-Euclidean geometry?
Can anyone help?> To whom should one pose the problemor or consult?
I shall acknowledge replies by a letter  GLN



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