Ibrahim ibn Sinan

Its life and its work

Ibrahim ibn Sinan was the son of Sinan ibn Thabit ibn Qurra (° v. 880 - † 943), doctor, mathematician and astronomer Persan, and the Al-Sabi grandson Thabit ibn Qurra Al-Harrani, known under the name of Thabit ibn Qurra, (° in 836 - † February 18th 901).

It is famous for its mathematical work, which brought a new vision of the geometry, being studied of which it was devoted, bringing significant développemants and inventing new methods. It continued the studies of Archimedes on the surfaces and volumes. He wrote comments on the Almageste of Ptolémée. Its work is known to us by the seven treaties which it published and by its “ Lettre on the description of the concepts ”.

Ibrahim ibn Sinan worked on the conic sections, more particularly studied the tangeantes with the circles, as well as the apparent movements of the Sun such as it are revealed by the geometry of the shades. Whereas it was only 17 years old, Ibrahim was interested in the various manners of expressing the hour thanks to the sun. It summarized its work in a treaty in which it analyzes the known data since Ptolémée and exposes its own theory on the solar movement. Following her grandfather, Ibrahim formulated a method to draw the curves required by the design of the sundials, which will remain a long time a reference.

The most important work of Ibrahim Ibn Sinan concerned the quadrature of the circle, where it introduced a method of integration more general than that of Archimedes. His/her grandfather Thabit ibn Qurra had started to consider the integration from a point of view different from that of the Greek mathematician, but had not completely been able to succeed. Its study had been exceeded by that of an Arab mathematician, Al-Mahani. Ibrahim recognized the fact (“the Al-Mahani study will remain more advanced than that of my grandfather, unless somebody of our family can exceed it”) and undertook to continue work of her grandfather. Its theory on the quadrature of the circle was simpler than that of Archimedes, and it will be exceeded only after the discovery of the integral calculus.

In its treaty “ To the measure of the circle ”, Ibrahim ibn Sinan manages to prove that the surface of a segment of the circle represents the four thirds of the surface of the registered triangle.

It was one of the Arab mathematicians of this time which was worried the most philosophy of mathematics, and wrote in particular a treaty on the analysis and the synthesis, pointing out that the contemporary geometricians had neglected the method of Apollonius.

There is not any doubt that its untimely death - he died in only 38 years - prevented from contributing to mathematical science a share more important than that of his/her famous grandfather. He nevertheless is considered, according to the dires of the historian of mathematics the German professor Fuat Sezgin, like “one of the most important mathematicians of the medieval Islamic world”.

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