Birthday

Happy birthday, tygerr!

E/NE 4: Right Down the Line

In Euclidean geometry, it's not too hard to verify the existence of rectangles. The discussion in the previous post leads up to the converse, which is the climax of this series of posts: if rectangles exist, then Euclid's parallel postulate holds. (Or, turning things around, there are no rectangles in hyperbolic geometry.) The proof is under the cut.

( Proving the Fifth )