(February 17, 2014 at 11:06 am)Rational AKD Wrote:(February 17, 2014 at 10:34 am)StuW Wrote: Maybe you should re-read the definition of coplanar
yes, 3 points are always coplanar. however, in the example you gave the lines (though they aren't technically lines) do not remain in the same plane. they curve outside the plane of the three points. because the lines curve they are not line segments, and because they curve outside the plane of the 3 points they are not coplanar either.
There are geometric spaces in which the sides of a triangle are coplanar yet the sum of the angles is greater or lesser than 180 degrees. I can't tell what you're responding to because in addition to a lengthy point by point reply, you screwed up the quote tags so badly it's impossible to follow who said what.
Oh, and if you're going to cite Kant as an authority, it's inappropriate to then claim that you don't have to provide a valid citation. That's just ass, and puts you back in the position of having your entire argument rest on a bare assertion, which invalidates the entire argument.
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