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Miklós Schweitzer 1955- Problem 9

Source:

October 8, 2015
college contests

Problem Statement

9. Show that to any elliptic paraboloid φ1\varphi_1 there may be found an elliptic paraboloid φ2\varphi_2 (other than φ1\varphi_1) and an affinity ϕ\phi which maps φ1\varphi_1 onto φ2\varphi_2 and has the following property: If PP is any point of φ1\varphi_1 such that ϕ(P)≠P\phi(P) \neq P, then the straight line connecting PP and ϕ(P)\phi(P) is a common tangent of the two paraboloids. (G. 18)
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