Numerically 

[Graphics:../Images/index_gr_7.gif]
[Graphics:../Images/index_gr_8.gif] [Graphics:../Images/index_gr_9.gif] [Graphics:../Images/index_gr_10.gif]
[Graphics:../Images/index_gr_11.gif] [Graphics:../Images/index_gr_12.gif] 0.6169031462060457`
[Graphics:../Images/index_gr_13.gif] [Graphics:../Images/index_gr_14.gif] 0.6476683937823835`
[Graphics:../Images/index_gr_15.gif] [Graphics:../Images/index_gr_16.gif] 0.6807351940095302`
[Graphics:../Images/index_gr_17.gif] 0.4239999999999968` 0.7163323782234956`
[Graphics:../Images/index_gr_18.gif] 1.875` 0.7547169811320754`
[Graphics:../Images/index_gr_19.gif] 3.1759999999999975` 0.7961783439490446`
[Graphics:../Images/index_gr_20.gif] 4.332999999999997` 0.8410428931875527`
[Graphics:../Images/index_gr_21.gif] 5.3519999999999985` 0.889679715302491`
[Graphics:../Images/index_gr_22.gif] 6.239000000000002` 0.9425070688030158`
[Graphics:../Images/index_gr_23.gif] 7.` 1.`
[Graphics:../Images/index_gr_24.gif] 7.641000000000001` 1.0626992561105206`
[Graphics:../Images/index_gr_25.gif] 8.168000000000001` 1.1312217194570136`
[Graphics:../Images/index_gr_26.gif] 8.587` 1.2062726176115803`
[Graphics:../Images/index_gr_27.gif] 8.904` 1.2886597938144329`
[Graphics:../Images/index_gr_28.gif] 9.125` 1.3793103448275863`
[Graphics:../Images/index_gr_29.gif] 9.256000000000004` 1.4792899408284024`
[Graphics:../Images/index_gr_30.gif] 9.302999999999999` 1.5898251192368842`
[Graphics:../Images/index_gr_31.gif] 9.271999999999998` 1.7123287671232879`
[Graphics:../Images/index_gr_32.gif] 9.169` 1.8484288354898337`
[Graphics:../Images/index_gr_33.gif] 9.` 2.`
[Graphics:../Images/index_gr_34.gif] 8.771` 2.169197396963124`
[Graphics:../Images/index_gr_35.gif] 8.488` 2.358490566037736`
[Graphics:../Images/index_gr_36.gif] 8.156999999999998` 2.5706940874035995`
[Graphics:../Images/index_gr_37.gif] 7.783999999999999` 2.808988764044944`
[Graphics:../Images/index_gr_38.gif] 7.374999999999998` 3.0769230769230775`
[Graphics:../Images/index_gr_39.gif] 6.936` 3.378378378378378`
[Graphics:../Images/index_gr_40.gif] 6.472999999999999` 3.7174721189591087`
[Graphics:../Images/index_gr_41.gif] 5.991999999999998` 4.0983606557377055`
[Graphics:../Images/index_gr_42.gif] 5.498999999999999` 4.524886877828054`
[Graphics:../Images/index_gr_43.gif] 4.999999999999999` 5.000000000000001`
[Graphics:../Images/index_gr_44.gif] 4.500999999999999` 5.52486187845304`
[Graphics:../Images/index_gr_45.gif] 4.007999999999999` 6.097560975609757`
[Graphics:../Images/index_gr_46.gif] 3.5269999999999992` 6.711409395973156`
[Graphics:../Images/index_gr_47.gif] 3.063999999999999` 7.352941176470589`
[Graphics:../Images/index_gr_48.gif] 2.624999999999999` 8.000000000000002`
[Graphics:../Images/index_gr_49.gif] 2.2159999999999993` 8.620689655172415`
[Graphics:../Images/index_gr_50.gif] 1.8429999999999995` 9.174311926605506`
[Graphics:../Images/index_gr_51.gif] 1.5119999999999993` 9.615384615384617`
[Graphics:../Images/index_gr_52.gif] 1.2289999999999994` 9.900990099009901`
2.220446049250313`*^-16 0.9999999999999996` 10.`
0.10000000000000023` 0.8309999999999997` 9.900990099009901`
0.20000000000000023` 0.7279999999999999` 9.615384615384615`
0.30000000000000027` 0.6970000000000001` 9.174311926605505`
0.40000000000000024` 0.7440000000000002` 8.620689655172413`
0.5000000000000002` 0.8750000000000004` 7.999999999999998`
0.6000000000000003` 1.096000000000001` 7.352941176470587`
0.7000000000000003` 1.413000000000001` 6.711409395973153`
0.8000000000000003` 1.8320000000000012` 6.0975609756097535`
0.9000000000000002` 2.359000000000001` 5.524861878453037`
1.` 3.` 5.`
Use this data to approximate the intersections.  How could you get better approximations without having to list thousands of points?

Converted by Mathematica      May 12, 2003