The Theory of Parallels
The concept of parallel lines has led to both the most fruitful and the most frustrating developments in plane geometry. Euclid (c. 330–275 B.C.) defined two segments to be parallel if no matter how far they are extended in both directions, they never meet. Note that he was interested in segments rather than lines. This follows the general preference of the time for finite objects. The idea of never meeting is, however, infinite in nature. How then does one determine if two lines are parallel?
KeywordsParallel Line Critical Function Hyperbolic Plane Hyperbolic Geometry Unique Line
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