I present a geometrical method that produces the fundamental holomorphic surface of the complex logarithm (classically obtained via analytic continuation) without any tools concerning the complex structure or the Covering Spaces theory. The only tools employed are elementary notions of (real) Differential Geometry and ordinary convergence of surface sequences.

Author Bio

Nikolaos Katzourakis is a postgraduate student of Theoretical Mathematics at University of Athens and this paper was written when he was an undergraduate at the same Institute, as the result of an idea during the undergraduate exams in "Complex Analysis". He was not supported by any specific program. His scientific interest stands within Differential Geometry, Algebraic Topology and their applications in Mathematical Physics. He has initiated a research program proposing a (mathematically) provable constructive geometrical model that globalizes the embedding theories of Multi-Dimensional Gravity (pre-print: ArXiv:math-ph/0407067).