Hasan bin Musa

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al-Hasan ibn Musa ibn Shakir Banu Musa, also Bani Musa, (810–873), (Arabic: الحسن بن موسى بن شاكر ) was a 9th century Persian mathematician and astronomer who lived in Baghdad.

He wrote The elongated circular figure which is a work on the ellipse. This book is lost except for a fragment in Hebrew of a compilation by Ibn al-Samh. From this fragment Rashed in Banu Musa, The Encyclopaedia of Islam VII (Leiden, 1993), 640-641, deduces that al-Hasan had two objectives. One objective was to measure a curved area while the other was to study the geometric properties of curves.

Rashed claims, that while Archimedes' texts were being translated into Arabic for the first time, the Banu Musa brothers (perhaps al-Hasan in particular) was trying to give new proofs of the Greek results as well as trying to prove results going beyond what the Greeks had achieved.

He, along with his two brothers, were instrumental in translating many scientific Greek and Pahlavi (Middle Persian) manuscripts into Arabic for al-Ma'mun. The Banu Musa brothers were among the first group of mathematicians to begin to carry forward the mathematical developments begun by the ancient Greeks. Those activities were carried out in the House of Wisdom

The most studied treatise written by the Banu Musa is Kitab marifat masakhat al-ashkal (The Book of the Measurement of Plane and Spherical Figures). This work became well known through the translation into Latin by Gherard of Cremona entitled Liber trium fratum de geometria. The treatise considers problems similar to those considered in the two texts by Archimedes, namely On the measurement of the circle and On the sphere and the cylinder.

The Banu Musa brothers took a definite step forward, where the Greeks had not; The Greeks had not thought of areas and volumes as numbers, but had only compared ratios of areas etc. The Banu Musa's concept of number is broader than that of the Greeks. For example they describe pi as:

"... the magnitude which, when multiplied by the diameter of a circle, yields the circumference."

The Banu Musa also introduce geometrical proofs which involve thinking of the geometric objects as moving. In particular they used kinematic methods to solve the classical problem of 'trisecting an angle'.

In astronomy the brothers made many contributions. They were instructed by al-Ma'mun to measure a degree of latitude and they made their measurements in the desert in northern Mesopotamia. They also made many observations of the sun and the moon from Baghdad. Muhammad and Ahmad measured the length of the year, obtaining the value of 365 days and 6 hours. Observations of the star Regulus were made by the three brothers from their house on a bridge in Baghdad in 840-41AD, 847-48AD, and 850-51AD.

[edit] Sources

Golden Age of Persia, Richard Nelson Frye, p162-163.
D El-Dabbah, The geometrical treatise of the ninth-century Baghdad mathematicians Banu Musa (Russian), in History Methodology Natur. Sci., No. V, Math. Izdat. (Moscow, 1966), 131-139.