Discussion:  All Topics in Geometry 
Topic:  Smartboard and Geometric Constructions 
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Subject:  RE: Smartboard and Geometric Constructions 
Author:  ihor 
Date:  Aug 30 2006 
> On Aug 30 2006, ihor wrote:
>A more significant
> mathematical
> point is to make sure that the students understand that
> a line
> represents an infinite set of points
On Aug 30 2006, Mathman replied:
Not to be argumentative,
> and since it has been forty years since I saw the stuff [Affine
> Geometry] and might well be wrong, but aren't "point" and "line"
> distinct? That is a foundation for duality, and although points may
> lie in a line, that does not make a line an infinite set of points.
> So, two points are necessary and sufficient to define one line [will
> lie on exactly one line], and two lines can intersect in only one
> point.
Ihor responds:
>but aren't "point" and "line"
> distinct?
I'm only talking about points whose order pairs satisfy the equation that is
represented by the line.
I think we have strayed from the orginal point which Susan answers very well in
an another reply to the Smartboard question.
 
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