Axiom talk:Parallel Postulate

I'm pretty sure that the parallel postulate is distinct from the Playfair's axiom. Can we double check this? --R payne77 05:54, 22 November 2008 (UTC)

Well yeah, technically it is "distinct" from it (it is equivalent to Proclus' note on Euclid I.31 ("only one straight line can be drawn through a point parallel to a given straight line") but this page does not claim Playfair's Axiom is the same as the parallel postulate, merely that it is "logically equivalent" to it. That is, you can prove either from the other using arguments following directly from the other 4 axioms. --Matt Westwood 08:34, 22 November 2008 (UTC)

... beg pardon I misread. Let me go away and rethink ... --Matt Westwood 08:35, 22 November 2008 (UTC)

... Actually I think you're right: according to this Wikipedia link, the "Parallel Postulate" is the name usually given to Euclid's 5th Postulate, rather than Playfair's Axiom.

IMO they could all be merged into one page, as they all effectively say "the same thing". Then we could insert a Redirect from "Parallel Postulate" and "Playfair's Axiom" as appropriate if we wanted to, and it would save any confusion. --Matt Westwood 08:42, 22 November 2008 (UTC)

Yeah, you're right. I misread the wolfram article on the parallel postulate when I made the page. I agree with Matt, we probably should just have one page for all the equivalent statements of the postulate. I vote we just have subheadings on Axiom:Euclid's Fifth Postulate for the parallel postulate and Playfair's axiom. Any others that people can think of? --Cynic 15:52, 22 November 2008 (UTC)

Loads. I know of at least 10. I'll get to it when I'm not quite so dopey. --Matt Westwood 17:10, 22 November 2008 (UTC)

... okay, this page has now been redirected to, and incorporated in, Axiom:Euclid's Fifth Postulate. --Matt Westwood 19:23, 22 November 2008 (UTC)