CDAM: Computational, Discrete and Applicable Mathematics@LSE

 CDAM Research Report, LSE-CDAM-2008-06

May 2008

Mathematics of Currency and Exchange: Arithmetic at the end of the Thirteenth Century

Norman Biggs

In Western Europe, a sophisticated banking system for the purposes of international trade had evolved by the end of the thirteenth century. It was based upon the `bill of exchange', which enabled an exporter of goods to receive payment in his own currency, by means of a balancing payment made in the currency of the importer. This paper discusses the arithmetical tools that were available for use in accounting for transactions made in different currencies. It is argued that algorithmic methods based on the Hindu-Arabic numerals were used at the higher levels of banking, in order to prepare tables of foreign exchange such as those collected by the Florentine banker, Francesco Pegolotti. On the other hand, the clerks who were responsible for routine book-keeping would have used a simple abacus and counters, and recorded their transactions in Roman numerals.

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