On the equivalence of Playfair's axiom to the parallel postulate
classification
🧮 math.HO
math.MG
keywords
axiomparallelplayfairpostulateequivalenceabsenceclassicalcollapses
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We show that the classical equivalence of Euclid's parallel postulate and Playfair's axiom collapses in the absence of triangle congruence. In particular, we construct a non-SAS geometry that models the Playfair axiom but not the parallel postulate.
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