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# In what type of geometry must parallel lines intersect?

Question #106861. Asked by gk9760. (Jul 05 09 7:08 PM)

Arpeggionist

If you believe the jokes, the answer is: in Boston's city streets.

 Jul 05 09, 7:16 PM
ArlingtonVA

Elliptic geometry, one form of non-Euclidian geometry.

"* In Euclidean geometry the lines remain at a constant distance from each other, and are known as parallels.
* In hyperbolic geometry they "curve away" from each other, increasing in distance as one moves further from the points of intersection with the common perpendicular; these lines are often called ultraparallels.
* In elliptic geometry the lines "curve toward" each other and eventually intersect."

Or, it could be Boston's city streets...lol

The treatment of parallel lines is the essential feature differentiating Euclidian from non-Euclidian geometry.

http://en.wikipedia.org/wiki/Non-Euclidean_geometry

 Jul 05 09, 7:30 PM

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