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