Sylvia Couchoud

Sylvia Couchoud is the author of a book on Egyptian mathematics.

The book Mathematical Egyptian women

Mathematics in Egypt of the Pharaons is mainly known for us through four papyri: the Papyrus Rhind, the Papyrus of Moscow, the Papyrus of Akhmîm and one of the Papyri Kahun. These documents all, published for a long time and having been the subject of various translations, are unfortunately completely dispersed in various libraries and there exists any overall edition, neither for the public, nor even of strictly professional use, which makes it possible to bring them closer between them.

The book, on 200 pages, reproduced, transcribed as an Egyptian and translated into French the essence of these hiéroglyphes and makes them accessible from now on to the general public. While going back directly to the sources, by means of photographic reproductions and by studying the whole of the translations, Sylvia Couchoud does a work of philology of the hieroglyphic language (see Liminaire p. 6), indexes the specific vocabulary which indicates the mathematical elements or concepts (drawn from the usual vocabulary while diverting the direction, or made up of words especially created). It rectifies, thus, several erroneous translations. At this stage, the translations would remain completely incomprehensible for a modern reader. Sylvia Couchoud, which is not historian of mathematics and the being does not claim at all, carries out necessary work and gives the equivalent, in our current language, of the regulations of the scribe.

That gives for example, for the R50 reference of the Papyrus Rhind (pp. 61-65):

Example of calculation of a round field of 9 khet.
Of how much is the surface of the field?
You will withdraw his ninth which is 1, it remains 8.
You will make in kind multiply 8 times 8. It occurs 64.
This is the surface of the field, namely 64 aroures.
To make as follows: 1,9, its 1/9, 1.
Withdraw it, it remains 8. 1,8. 2,16. 4,32. 8,64.
The surface of the field is 64 aroures.

A drawing in the reference R48 (of which the form evokes the Quadrature of the circle) specifies the step (p. 7).

The regulation of the scribe Ahmosé amounts replacing the surface of a round field of 9 khet diameter by the surface of a square field of 8 khet on side. The equivalent, in our current language, is to use for pi the following fractional approximation:

4 X (8/9) X (8/9), is 3,16, which gives on pi an accuracy of 0,6%.

If this text does not constitute a conceptual definition of pi, one cannot reduce the regulation exposed to a strictly empirical step to solve a practical problem. Indeed, they is only with 9 and 8, the figures precisely chosen by the scribe, that the approximation is precise, whereas one often does not find a field round of 9 khet diameter in practice! The pedagog at the head has something which resembles the formula S = (64/81) X (D X d), but it does not have the means of writing it.

Sylvia Couchoud, also, wrote a glossary of 124 mathematical terms which one regularly finds in the papyri (pp. 194-204). This glossary, which include/understand the hiéroglyphes, their transcription as an Egyptian and the translation in French, are a convenient tool to approach any mathematical text in hiéroglyphes.

Sylvia Couchoud written (p. 1-2 and p. I):

There are however an important difference between Greek mathematics and those of Pharaonic Egypt. The Greeks were interested in the formulas and to the theories and they brought to their demonstrations evidence. The Egyptians, for their part, were interested above all in the results of their calculation and if they also sought evidence for the latter, it was only with an aim of showing their exactitude numérique.

I dedicate this work with all my admiration and my recognition with Ahmosé, the scribe which recopied, four thousand years ago, this papyrus mathematical which one calls today the Papyrus Rhind.

Reception

Two account-returned of this book can be located in reviews at reading panel:

the first, rather critical, explains why one of principal the defects of this book is to be satisfied to fly over the existing literature, and its lack of retreat compared to certain work;

the second, much more critical still, examines in detail a certain number of proposals of the author to say the weakness of it. The author of the “review” thus writes, in connection with the theses of Couchoud on the comprehension of the π number by the Egyptians, that with regard to the circle, to compare to an approximation of π/4 the ratio from 64 to 81 is not justified: indeed it is about a relationship between surfaces, but letter pi indicates a relationship between lengths (circumference and diameter) and nothing does not say there to us that the Egyptians passed from the one to the other while knowing to recognize same the rapport. He finishes his comment in these terms: the conclusion suggested pours unnecessarily in the exaggeration. One cannot say that the Egyptian had " all outils" to solve the problems " more complexes" of geometry and arithmetic, which he knew " powers and roots, " whereas it is question only of squares, that it solved " equations of the second degré" , that the surface of the sphere " hardly had secrecies for him, " or that he knew " fundamental laws of the mathématiques" (?!); and as regards the " evidence, " it - should it was not a question be said? - that checks numérique. He adds however that this work can give to the Egyptologists opportunity of consulting directly in the language of the hiéroglyphes calculative texts which differently are dispersed, and some had been badly lus.

Works

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