"Introduction to Non-Euclidean Geometries"

The idea that distinguishes Euclidean from non-Euclidean geometries is the truth of what is known as the "Fifth Postulate." Basically, this postulate states that, given a line and a point not on the line, it is possible to draw exactly one line through the point that is parallel to the first line.

This seems intuitively obvious, but all attempts to prove it using basic axioms of geometry have been unsuccessful.

So what if the Fifth Postulate turned out to be false? If we can't prove something, it may be because it simply isn't true.

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