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Abstract. In this paper, the conjecture on the Zalcmanness of C n (n ≥ 2) and (C * ) 2 , which is posed in our previous work, is proved in the case where the derivatives of limit holomorphic curves are bounded. Moreover, several criteria for normality of families of holomorphic mappings are given.

We prove that the necessary and sufficient conditions given by S. Takahashi for the Nevanlinna-Pick-Caratheodory-Fejer interpolation problem can be obtained from the theory of D. Sarason.

Pappus’s theorem is a classical result in geometry. We present four proofs for Pappus’s theorem. Each proof makes use of different tools and techniques.