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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.

Richard Barrans Jr.



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