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Abstract: It has been at various times proposed in regard to Problem 10 of the Moscow Mathematical Papyrus that Egyptian scribes had developed a computational algorithm by which they could calculate the circumference of a circle of known diameter length. It has also been proposed at various times that the 7:22 ratio between a circle’s diameter and its circumference was known by the Egyptian scribes at a surprisingly early period. The present paper explores currently available evidence that lends support to each of these propositions. [Copyright &y& Elsevier]

Abstract: The algorithms used in Arabic and medieval European mathematics for extracting cube roots are studied with respect to algebraic structure and use of external memory (dust board, table, paper). They can be separated into two distinct groups. One contains methods used in the eastern regions from the 11th century, closely connected to Chinese techniques, and very uniform in structure. The other group, showing much wider variation, contains early Indian methods and techniques developed in central and western parts of the Arabic areas and in Europe. This study supports hypotheses previously formulated by Luckey and Chemla on an early scientific connection between China and Persia. [Copyright &y& Elsevier]

Abstract: Is a mathematical problem a cultural invariant, which would invariably give rise to the same practices, independent of the social groups considered? This paper discusses evidence found in the oldest Chinese mathematical text handed down by the written tradition, the canonical work The Nine Chapters on Mathematical Procedures and its commentaries, to answer this question in the negative. The Canon and its commentaries bear witness to the fact that, in the tradition for which they provide evidence, mathematical problems not only were questions to be solved, but also played a key part in conducting proofs of the correctness of algorithms. [Copyright &y& Elsevier]

The Old Babylonian mathematical tablet YBC 4652 contains a series of related problems stated together with their answers. In this paper, we propose a procedure for determining the solutions to these problems and consider the pedagogy underlying the mathematics. © 2002 Elsevier Science (USA).L'ancienne tablette mathe´matique babylonienne YBC 4652 contient une se´rie de proble`mes avec leurs re´ponses. Dans cet article, nous proposons une proce´dure pour de´terminer les solutions de ces proble`mes et conside´rons la de´marche pe´dagogique sous-jacente aux mathe´matiques. © 2002 Elsevier Science (USA).MSC 1991 subject classification: 01A17. [Copyright &y& Elsevier]