Re: [MLUG - DISCUSSION] In Math, Computers Don't Lie. Or Do They?

[Jonathan King <EMAIL:PROTECTED>]

On Thu, 8 Apr 2004, Mike Miller wrote:

> On Thu, 8 Apr 2004, Jonathan King wrote:
> 
> > > The line would have to hit either a side or a vertex.
> >
> > Atually, a side and a vertex or a side and a side (these are lines).
> 
> Sorry, I thought it had to extend infinitely in only one direction.

Well, lucky for you it doesn't; otherwise Euclid would have been 
dead wrong if I understand the problem correctly. :-)
 
> Can one make use of the following:  draw line segments from the
> interior point to the vertices.  This divides the larger triangle
> into three smaller triangles.  Then you can simplify the problem
> by noting that the line must pass through the interior of at least
> one of the three triangles.

I'm not sure I see the simplification.  I mean, sure, I see it, but 
I think it's really resistant to proof.  With more effort than I 
should have spent, it looks to me like this is in fact a problem 
that Hilbert did have to go back and solve.  I think it is 
equivalent to Hilbert's Fourth Axiom of Order.  According to:

http://www.friesian.com/space.htm

Hilbert needed to state the following fairly toolish postulate:

    Let A, B, C be three points that do not lie on a line and let a 
    be a line in the plane ABC which does not meet any of the points 
    A, B, C. If the line a passes through a point of the segment AB, 
    it also passes through a point of the segment AC, or through a 
    point of the segment BC.

...which implies the truth of the Inebriated Mathematician's
Proposition.  Note also that in a way reminiscent of Euclid's
parallel postulate, this *sounds* like something you could prove,
but if Hilbert couldn't do it...don't try this at home.

jking


_______________________________________________
discussion mailing list
EMAIL:PROTECTED
http://mlug.missouri.edu/mailman/listinfo/discussion