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too complicated to be written here. Click on the link to download a text file. |
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X(3), X(6), X(17), X(18), X(397), X(398), X(485), X(486) other points below. |
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Geometric properties : |
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K1203 is a cuspidal KHO-cubic. See K1191 for explanations and also CL075. K1202 is another similar cubic. Its KHO-equation is : x^2 (y + 2z) - 9y^3 = 0. K1203 has a cusp at O with cuspidal tangent the Euler line and a point of inflexion at K with inflexional tangent passing through X(382).K1203 meets the Kiepert hyperbola at X(17), X(18), X(485), X(486) and two imaginary points on the line X(6)X(30) with KHO-coordinates (±3i,1,-1). Q1, Q2 lie on the cubic, on the line X(6)X(631), and their KHO-coordinates are (±1,1,4). The tangentials of : • X(397), X(398) are X(17), X(18). • X(17), X(18) are (±3,4,30). • X(486), X(485) are (±√3,2,11). • Q1, Q2 are (±1,2,35). • (±3,5,60) are (±3,10,495). *** More generally, if u : v: w are the KHO-coordinates of a point T (different from O and K) on K1203, then the point T(n) = (2 (-1)^n u^3 , 2^(1 + n) u^2 v , 2^n v (-u + 3 × 2^n v) (u + 3 × 2^n v)) is its nth tangential. Obviously, T(0) = T and T(n + 1) is the tangential of T(n). Conversely, T(n - 1) is the pretangential of T(n). |
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