The Non-Euclidean geometry reference article from the English
Wikipedia on 24-Jul-2004 (provided by Fixed Reference: snapshots
of Wikipedia from  Non-Euclidean geometry  You can make a
difference by sponsoring a child  The term non-Euclidean
geometry (also spelled: non-Euclidian geometry) describes both
hyperbolic and elliptic geometry, which are contrasted with
Euclidean geometry. The essential difference between Euclidean
and non-Euclidean geometry is the nature of parallel lines. In
Euclidean geometry, if we start with a point A and a line l,
then we can only draw one line through A that is parallel to l.
In hyperbolic geometry, by contrast, there are infinitely many
lines through A parallel to l, and in elliptic geometry,
parallel lines do not exist. (See the entries on hyperbolic
geometry and elliptic geometry for more information.)  Another
way to describe the differences between these geometries is as
follows: consider two lines in a plane that are both
perpendicular to a third line. In Euclidean and h