Practical Geometries in Islamic Countries: the example of the division of plane figures
Résumé
The division of plane figures is a geometrical chapter developed in numerous works written in Arabic. In the extension of Greek practices, this chapter is also found in original developments in Islamic countries. The aim of the presentation is to show the diversity from several books of the Muslim Orient and Occident from the 9th century until the 14th century. This diversity is first based on the multiple origins of the problems. They are linked, among others, to the practices of craftsmen, architects, or jurists. For example, jurists had to decide on the sale or the sharing of fields. To divide a geometrical figure in a certain number of similar figures is an important problem for the decorators who embellished palaces, madrasas, and other mosques and mausoleums. Moreover, these problems are illustrated in some writings of eminent geometers. This diversity also expresses itself by the wealth of procedures of construction and resolution for which the whole mathematical knowledge is included.
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