Ibrahim ibn Sinan was an Arab astronomer and mathematician. He is known for his studies of geometry and in particular of tangents to circles; he also made advances in the quadrature of the parabola and the theory of integration, generalizing the work of Archimedes, which was unavailable at the time.

Background

Ibrahim ibn Sinan was born c. 908 in Baghdad, Abbasid Caliphate (now in Iraq). Born into a family of celebrated scholars, he was the son of Sinan ibn Thabit, a physician, astronomer, and mathematician, and the grandson of Thabit ibn Qurra, also a mathematician.

Education

Ibn Sinan was productive from an early age; according to his autobiography, he began his research at 15, and studied geometry and in particular tangents to circles. He also studied the apparent motion of the Sun and the geometry of shadows.

Career

Although Ibn Sinan's scientific career was brief - he died at the age of thirty-eight - he left a notable body of work, the force, and perspicuity of which have often been underlined by biographers and historians. This work covers several areas, such as tangents of circles, and geometry in general; the apparent motions of the sun, including an important optical study on shadows; the solar hours; and the astrolabe and other astronomical instruments.

His study of the parabola followed directly out of the treatment given the problem in the work of his grandfather. Thabit ibn Qurra had already resolved this problem in a different way from that of Archimedes. Although his method may have been equivalent to that of summing integrals, the approach was more general than that of Archimedes in that the intervals of integration were no longer divided into equal subintervals. Thabit’s demonstration was lengthy, however, containing twenty propositions. Another mathematician, one al-Mahanni, had given a briefer one but Ibn Sinan felt it to be unacceptable that “al Mahanni’s study should remain more advanced than my grandfather’s unless someone of our family can excel him.” He therefore sought to give an even more economical demonstration, one that did not depend upon reduction to the absurd. The proposition on which Ibn Sinan founded his demonstration, and which he took care to prove beforehand, is that the proportionality of the areas is invariant under affine transformation.

Ibn Sinan’s originality in his investigation is manifest. It was with that same independence of mind that he intended to revive classical geometric analysis in order to develop it in a separate treatise. By virtue of that study, the author may be considered one of the foremost Arab mathematicians to treat problems of mathematical philosophy. His attempt has the form of a critique of the practical geometry in his own times.

In his work, Ibn Sinan proposed two tasks simultaneously, the one technical and the other epistemological. On the one hand, the purpose was to provide those learning geometry with a method (tariq) which could furnish what they needed in order to solve geometrical problems. On the other hand, it was equally important to think about the procedures of geometrical analysis itself and to develop a classification of geometrical problems according to the number of the hypotheses to be verified, explaining the bearing, respectively, of analysis and synthesis on each class of problems.

Achievements

Religion

Ibn Sinan was affiliated with Islam.

Views

Quotations:
“I have found that contemporary geometers have neglected the method of Apollonius in analysis and synthesis, as they have in most of the things I have brought forward, and that they have limited themselves to analysis alone in so restrictive a manner that they have led people to believe that this analysis did not correspond to the synthesis effected.”

Personality

Quotes from others about the person

F. Sezgin: "Ibn Sinan was one of the most important mathematicians in the medieval Islamic world."

R. Rashed: "Considering both the problem of infinitesimal determinations and the history of mathematical philosophy, it is obvious that the work of ibn Sinan is important in showing how the Arab mathematicians pursued the mathematics that they had inherited from the Hellenistic period and developed it with independent minds. That is the dominant impression left by his work."

Connections

It is not known whether Ibn Sinan was married or not.