One may make a number of comments regarding these plots . Firstly , the symmetry of the function under the interchange of u and v is apparent ( and is manifest in the actual data ) . Secondly , for the values of w considered , for small u , v the remainder function takes a large negative value for w large , and increases as w decreases . The order of these hyper - surfaces reverses as u or v increase , and for large values of these variables , the remainder function becomes increasingly negative ( as of course required by the symmetry property and the behaviour at large u ) . For all three variables large , the remainder function approaches a constant which is equal to the asymptotic value of F 6 ( u ) ( about −0.67 ) . In general , it is apparent from Figures 8 - 10 that the remainder function is rather smooth for all values of the cross - ratios .