Question:
What is the difference between Euclidian and
Non-Euclidian geometry and what are some examples of each?
Replies:
Well, the whole difference between Euclidean and other geometries is their
treatment of parallel lines. In Euclidean (plane) geometry, parallel lines
never meet, and they are always separated by the same distance. In
Riemannian (elliptical) geometry, there are no parallel lines, as any two
straight lines will always meet somewhere. This is similar to what happens
to longitude lines on the earth's surface. The longitude lines on the
earth are not parallel; they are sections describing the intersection of
the earth's surface with planes that all intersect at the earth's axis. In
Lobachevskyan (hyperbolic) geometry, non-intersecting straight lines can
exist, and they will not always be the same distance from each other.
There will be some points that are closest to each other, and the lines
will ever diverge away from those points.
I'm not sure this fully answers your question. If it doesn't, clarify and
ask again.
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