From: utzoo!decvax!harpo!zeppo!wheps!ihnss!ihuxq!grumpy
Newsgroups: net.math
Title: solution to construction problem
Article-I.D.: ihuxq.130
Posted: Fri Jun 25 13:11:37 1982
Received: Mon Jun 28 05:17:32 1982


     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