Take any four points in space. Draw all lines connecting pairs of them. Then draw all lines connecting pairs of points on those lines.
Can the resulting set of points cover all of space?
(In reply to
Smart guys Help by Hugo)
Hugo,
The point (1,1,1) lies on the line connecting (1/2,1/2,0) and (0,0,-1). The point (1/2,1/2,0) lies on the line connecting (1,0,0) and (0,1,0), and the point (0,0,-1) lies on the line connecting (0,0,0) and (0,0,1).
As for all (x,y,z) where x, y, and z are greater than 1, try connecting (x,y,z) to the entire line through (1,0,0) and (0,1,0). That makes some kind of half-plane. Hopefully you see that that plane intersects the z-axis at some point P. Going backwards, you can take P, and the point Q at which the line connecting (x,y,z) and P intersects the xy-plane. P and Q generate the point (x,y,z). P is found on the line connecting (0,0,0) and (0,0,1), and Q is found on the line connecting (1,0,0) and (0,1,0).
re: Smart guys Help
