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In classical or Euclidean plane geometry two points defines exactly one line. On a sphere two points can define infinitely many lines only one of which will represent the shortest distance between the points. On other curved surfaces, or in non-Euclidean geometries, the number of lines determined by two points can vary.

Even in the Euclidean plane, two points determine infinitely many lines that are not straight!

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βˆ™ 2011-12-22 15:14:01
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Q: How many different lines are determined by two points?
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