On 6/23/2015 10:36 PM, David Wilson wrote:
Thanks, Dr. Helenius.
I was always dissatisfied with the standard 2d picture because the lines have spurious R^2 intersection points that aren't Fano points. Your construction provides a neat model of with congruent lines and Fano topology.
You're welcome, but I'm afraid my construction is defective: it's very symmetrical, and the symmetry introduces three spurious intersections. As circles 5 and 6, for example, (the one with center on the x-axis and the one at theta = 120 degrees) tilt inward, they eventually cross the theta = 60 (or 240) degree plane where they will meet on circle 3. But in their final position they cross that plane twice, and they meet at both points. Perhaps this can be fixed by altering the construction slightly; say by giving the initial three circles a common twist (so the propeller shape they make actually works as a propeller), destroying the bilateral symmetry. But that's a lot more complicated to work out and I literally do have a plane to catch. -- Fred W. Helenius fredh@ix.netcom.com