From: rusin@vesuvius.math.niu.edu (Dave Rusin) Newsgroups: sci.math Subject: Re: Geometry - Line System Problem Date: 26 Aug 1997 16:01:50 GMT JamesBradleyHall wrote: > This system of lines has the following properties. Draw the minimum > number of lines in the system. > > 1. There exists a line and every line is point set. > 2. If P and Q are two points, there is one and only one > line containing them. > 3. Every line contains exactly three points. > 4. Every two lines has a point in common. > 5. No line contains all points. Gregory A Greenman wrote: >I don't think this problem has a solution, transcendental or not. >Two assumptions that most people will probably make that the rules don't >actually impose are: > >1. All lines are straight. >2. All points lie in a plane. > >Unfortunately, I don't see how removing either of these two assumptions >changes the situation. At the risk of completing the first poster's homework let me ask you to consider this famous diagram: o A *** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * **** **** * * **** * ****** * * *** * *** **** * *** *** * ** *** * ** B o* * *o C ** * * * ** ** * * * ** ** * * * * * * * * * * ** * * * o D * * * * * * * * * * * * * * * * * ** * * * * * * ** * * * ** * * ** * * * * * * *** * ** * * * * *** * *** * * * * *** * *** * * * * ***** * ****** * * * * ******* * * o*********************************o**********************************o E F G Here there are seven points A, ..., G and seven lines, where a "line" is the set of three points in one of the seven "*" paths (the sides and bisectors of the triangle as well as the circle). Look up "incidence geometry", "projective plane", "finite geometry", "Fano plane", etc. dave