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Mathematics

Parallel Lines: 1) I've been told that parallel lines never meet - except at infinity. 2) Also that a straight line is a circle of infinite radius. 3) Surely if you get two infinitely large circles such that they don't overlap, at their closest point they are straight (as per 2) and parallel yet must both meet (by 1) and not as per 3) - not overlapping. Any suggestions? (I'm confused!)
Accepted:
November 5, 2008

Comments

Thomas Pogge
November 16, 2008 (changed November 16, 2008) Permalink

I think your #1 should go. If you drive a sled through the snow, the two lines you draw in the snow will never meet, never get closer to each other, even if you drive on forever. If you have two intersecting lines and close the angle toward zero, then at the limit the lines will have the same direction ... but at that limit they will also coincide (be identical) and hence not be parallel.

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