5 Apr
2012
5 Apr
'12
9:55 a.m.
On Thu, Apr 5, 2012 at 11:42 AM, Dan Asimov <dasimov@earthlink.net> wrote:
But I'm puzzled by the comment that all circles pass through the "line at infinity" in two points, since one example of a circle (in the usual sense) in CP^2 is the set {[exp(it), 0, 1] in CP^2 : t in [0,2pi)}, which intersects x+y+z in only one point, [-1,0,1]. Or am I missing something?
By "circle", he means a conic in CP^2 whose intersection with the embedded R^2 (that is, x real, y real, z = 1) is a circle. These all have equal coefficients for x^2 and y^2, so they all pass through the points (1, i, 0) an d(1, -i, 0). Andy