To explain: in projective geometry, you allow points whose coordinates are 1/0. It basically turns the real number line into an infinitely large circle (positive infinity and negative infinity are the same).,(reply>), Well, in two or more dimensions, that's not a hundred percent true. In the projective plane, the point (5/0,3/0) is different from (1/0,1/0). A better way to think about the projective plane is, you write [a:b:c] instead of (a/c,b/c), and say two triples are the same if you can multiply each by a constant to get the other. So the two points I mentioned would be [5:3:0] and [1:1:0]. You just can't have all three coordinates be zero at once.<br>So it's like a plane made of proportions.<br>(What you used to call (a,b) now gets called [a:b:1] or [2a:2b:2] or [-a,-b,-1], etc. All the points with zero in the third coordinate are "new" points "at infinity".)