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The origin and mathematical treatment of the rhumb line in the sixteenth century

By: Henrique Leitão
From: Univ. Lisbon
At: Complexo Interdisciplinar, Anfiteatro
[2010-04-28] 11:30

The fundamental concept in the mathematical theory of navigation is the rhumb line (later called loxodromic curve). It was originally proposed in 1537 by the Portuguese cosmographer and mathematician Pedro Nunes (1502-1578) and further developed by him in a series of works until 1566. The idea spread very rapidly in Portugal and elsewhere. Although the importance of this notion in the history of navigation has been acknowledged many times, much less has been said about its importance in the history of mathematics. In fact, from a mathematical point of view the rhumb line introduced novel and very difficult problems: a never-ending spiral inscribed in a spherical surface, the pre-calculus study of this curve demanded a great amount of ingenuity, a number of approximations, and a delicate mix between formal proofs and practical knowledge. In this talk I will describe how Pedro Nunes tried to overcome these difficulties, and how this problem challenged mathematicians for over a century.