Subject: Re: [HM] When is Playfair's postulate important?
From: William C Waterhouse (wcw@math.psu.edu)
Date: Fri Jan 14 2000 - 15:21:16 EST
On Thu, 13 Jan 2000, Daina Taimina <dt34@cornell.edu> asked
whether there is a place where it is more natural to use the
uniqueness of parallels rather than other equivalents of the
parallel postulate. One that seems to me to fit that description
is the construction of a parallelogram.
That is, we start with segments AB, BC not on one line, and
we want a (the?) parallelogram with those as two sides. The
obvious thing to do is to take lines AP parallel to BC and
CQ parallel to AB; these meet, since the lines AP and AB are
different and so AP cannot be parallel to CQ.
William C. Waterhouse
Penn State
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