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 Discussion: All Topics 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.