Going the distance [2D geometry]
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One of the fun aspects of non-Euclidean geometries is discovering how familiar shapes change under new rules. The new rules mean we have to think about distances differently than in the world Euclid described. The author looks at a couple of simple 2D geometries that obey different distance rules than those that Euclid described.
[1] E. Allgower,et al. Numerical Continuation Methods , 1990 .