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Conventions for recreational problems in Fibonacci’s {\it Liber abbaci}. (English)
Arch. Hist. Exact Sci. 65, No. 2, 155-180 (2011).
Leonardo of Pisa, otherwise known as Fibonacci, produced his {\it Liber abbaci} in 1202. One interest in the recreational mathematics therein has been to see elements of the modern concepts of systems of linear equations and negative numbers. This paper is concerned with Leonardo’s construction of the problems, or, as some would say, riddles. The author identifies three conventions that they follow, such as: “Data in problems are usually small integers. A consequence of this is that solutions are relatively messy (for example, non-integers)." It is argued, contra some other accounts, that these conventions are in fact rules which had to be followed rather than simply a natural way of constructing problems. This assumption is shown to help explain Leonardo’s choice of problems among the possible ones that could be constructed, especially those in which, alongside an insoluble problem, he wishes to provide a very similar but soluble example. It is also suggested that Leonardo had no general formula or algorithm behind the construction of his problems; in some cases he appears to have stumbled across the appropriate data.
Reviewer: Albert C. Lewis (Austin)
Classification: A30 A20
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