grumpy (06/25/82)
I have found a way to construct a line parallel to two given
parallel lines through a given point not on either.
My appoach really doesn't require a pencil or a straight edge!
It does, however, involve paper folding!
First fold a crease for CD perpendicular to one of the given
lines AB A'B' by superimposing part of one of the given lines on
itself (see figure), then fold a crease through the given point G
for a line EF perpendicular to CD. That line is parallel to AB
and A'B' and is the required line.
E
---------------------------------------
\ \ \
\ A . A'. \ \
\ \ \ \ \
\ \ \ \ \
C \-------\----\------------\-----------\ D
\ \ \ \ \
\ \ \ \ \
\ B . B'. G . \
\ \ \
---------------------------------------
F
This idea came from "Modern Geometries" by James R. Smart
Michael E Bentz
Bell Labs
Indian Hill West
(312) 979-1026
...!ihnss!ihuxq!grumpy