Re: Can any triangle be "point-projected" onto any other triangle?

On Aug 5, 1:48 am, Phil Carmody <thefatphil_demun...@xxxxxxxxxxx>
wrote:
Robert Israel <isr...@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx> writes:
Phil Carmody <thefatphil_demun...@xxxxxxxxxxx> writes:

Hero <Hero.van.Jind...@xxxxxx> writes:
Phil wrote:
Hero writes:
Hi kj,

so the new question might be, given two arbitrary triangles (size
and
form) - can we position them in space, so that the lines connecting
corresponding corners will meet in a point?
(Which corners correspond?)

Anyhow, it would be nice, if You tell us a bit more.
Why or what for You are looking into this problem?
What are Your own results?

Trivial - line up 4 of the points.

When i take arbitrarily two triangles of equal form and size, which
points i can line up, so, that the lines meet in one point?

If both trianges are equilateral and the same size, then you're
screwed. Otherwise just take any two corners from each such that
the altitude of the third corners are different and line them up.

It's easy with congruent triangles: just reflect through the point
where you want the points to intersect.

Rotate about.

OK, I did that. Now what?

Robert Israel israel@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada



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