Graph Without Crossing LinesDate: 7/19/96 at 11:41:42 From: SURGICON LTD Subject: Graph Without Crossing Lines Dear Dr. Math, there are three houses 1 2 3 and there are three utilities gas water electric How can you connect the three houses individually to the three utilities without crossing your lines? (You have to draw a line from each house to each of the utilities without the lines ever crossing.) Thanks, Tone Date: 8/15/96 at 10:51:46 From: Doctor Patrick Subject: Re: Graph Without Crossing Lines Hi, sorry to tell you this, but that problem is impossible on most normal surfaces. The only one I know of where it will work is what is called a torus--which is basically a doughnut-shaped figure with a hole in the center. If you can, try the problem again on a surface like that and see what happens. Since a torus might be hard to come by, you can cut a hole in the center of the paper and allow lines to go onto both sides and through the hole onto the other side. Why do you think it works in this shape? -Doctor Patrick, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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