It is well-known the solution to the problem of connecting nine dots, arranged in three rows of 3 dots, with four straight lines, without lifting up the pencil from the paper where they are drawn, and without any tricks at all, like folding the paper, etc...

           o        o        o


           o        o        o


           o        o        o

The question is: given the nine dots above, is it possible to connect them with only 3 straight lines ? The restrictions are the same, that is, without lifting up the pencil from the paper where they are drawn, no tricks allowed, and if you retrace a line, you must count one more line.

Prove your answer!

Note: this is a revisit to the problem Nine Dots already posted in this site and you can use that drawing for reference.

It is possible, and rather trivial, if we do not limit ourselves to Euclidean geometry.  In spherical geometry, all parallel lines intersect (lines in spherical geometry are great circles).  Thus three parallel lines solve the problem in spherical geometry.

Posted by Brian Smith on 2005-07-15 01:23:15