1. These three and the identity permutation leave the cross ratio unaltered. 2. M�bius transformations satisfy exactly the same estimates, since M�bius transformations preserve the cross ratio . 3. In fact, every such invariant is expressible as a function of the appropriate cross ratio . 4. Could you give a proof that the cross ratio is the image of z _ 4? 5. I don't understand how the cross ratio answers when 4 points in projective line are projectivly equivalent. 6. The cross ratio of four different points is real if and only if there is a line or a circle passing through them. 7. Every four collinear points with rational coordinates have a rational cross ratio , so the Perles configuration cannot be realized by rational points. 8. :Afraid not, the cross ratio you get from joining opposite corners and projecting lines will be the same as for a square. 9. Modern use of the cross ratio in projective geometry began with Lazare Carnot in 1803 with his book " G�om�trie de Position ". 10. How can the cross ratio , a scalar, be the image of a map on the projective line, a point defined by two coordinates?
Mobile