## Al - Biruni

### Abu Arrayhan Muhammad ibn Ahmad al - Biruni

Born: 15 Sept 973 in Kath, Khwarazm (now Khorezm province, Uzbekistan.)

Al - Biruni is one of the major figures of Islamic mathematics. He contributed to astronomy, mathematics, physics, medicine and history.

Abu Rayhan al - Biruni was born in Khwarazm, a region adjoining the Aral Sea now known as Karakalpakstan. The two major cities in this region were Kath and Jurjaniyya. Al - Biruni was born near Kath and the town were he was born is today called Biruni after the great scholar. He lived both in Kath and in Jurjaniyya as he grew up and we know that he began studies at a very early age under the famous astronomer and mathematician Abu Nasr Mansur. The total number of works produced by al - Biruni during his lifetime is impressive. It is estimated, that he wrote around 146 works with a total of about 13,000 folios (a folio contains about the same amount as a printed page from a modern book). The range of al - Biruni’s works covers essentially the whole of science at his time. We know certain dates in al - Biruni's life with certainty for he describes astronomical events in his works which allow accurate dates and places to be determined. By the age of seventeen al - Biruni was engaged in serious scientific work for it was in 990 that he computed the latitude of Kath by observing the maximum altitude of the sun. His description of an eclipse of the moon on 24 May 997 which he observed at Kath means that he had returned to his nativecountry by this time. The eclipse was an event that was also visible in Baghdadand al - Biruni had arranged with Abu'l - Wafa to observe it there. Comparing their timings enabled them to calculate the difference in longitude between the cities. We know that al - Biruni moved around frequently during this period for by 1000 he was at Gurgan being supported by Qabus, the ruler of the Ziyarid state. He dedicated his work Chronology to Qabus around 1000 and he was still in Gurgan on 19 February 1003 and 14 August 1003 when he observed eclipses of the moon there. We should record that in the Chronology al - Biruni refers to seven earlier works which he had written: one on the decimal system, one on the astrolabe, one on astronomical observations, three on astrology, and two on history. His most famous work India was written as a direct result of the studies he made while in that country.

The India is a massive work coveringmany different aspects of the country. Al - Biruni describes the religion and philosophy of India, its caste system and marriage customs. He then studies the Indian systems of writing and numbers before going on to examine the geography of the country. The book also examines Indian astronomy, astrology and the calendar. The book might have been written, when al - Biruni was in India with Mahmud Ghaznavid during Mahmud's military excursions into India. It is likely that al - Biruni was essentially a prisoner of Mahmud and was not free to leave and it meant that al - Biruni was taken to that country by Mahmud. From around 1022 Mahmud's armies began to have success in taking control of the northern parts of India and in 1026 his armies marched to the Indian Ocean. Al - Biruni seems only to have been in the northern parts of India, and we are uncertain how many visits he made, but observations he made there enabled him to determine the latitudes of eleven towns around the Punjab and the borders of Kashmir.

Al - Biruni studied Indian literature in the original, translating several Sanskrit texts into Arabic. He also wrote several treatises devoted to certain aspects of Indian astronomy and mathematics which were of particular interest to him. Al - Biruni was amazingly well read, having knowledge of Sanskrit literature on topics such as astrology, astronomy, chronology, geography, grammar, mathematics, medicine, philosophy, religion, and weights and measures. One of the most important of al - Biruni's many texts is Shadows which he is thought to have written around 1021.The contents of the work include the Arabicnomenclature of shadeand shadows, strange phenomena involving shadows, gnomonics, the history of the tangent and secant functions, applications of the shadow functions to the astrolabe and to other instruments, shadow observations for the solution of various astronomical problems, and the shadow - determined times of Muslim prayers. Shadows is an extremely important source for our knowledge of the history of mathematics, astronomy, and physics. It also contains important ideas such as the idea that acceleration is connected with non - uniform motion, using three rectangular coordinates to define a point in 3 - space, and ideas that some see as anticipating the introduction of polar coordinates.

The book details the mathematical contributions of al - Biruni. These include: theoretical and practical arithmetic, summation of series, combinatorial analysis, the rule of three, irrational numbers, ratio theory, algebraic definitions, method of solving algebraic equations, geometry, Archimedes' theorems, trisection of the angle and other problems which cannot be solved with ruler and compass alone, conic sections, stereometry, stereographic projection, trigonometry, the sine theorem in the plane, and solving spherical triangles.

Important contributions to geodesy and geography were also made by al-Biruni. He introduced techniques to measure the earth and distances on it using triangulation. He found the radius of the earth to be 6339.6 km, a value not obtained in the West until the 16th century. His Masudic canon contains a table giving the coordinates of six hundred places, almost all of which he had direct knowledge. Not all, however, were measured by al -Biruni himself, some being taken from a similar table given by al - Khwarizmi. The author of remarks that al - Biruni seemed to realise that for places given by both al - Khwarizmi and Ptolemy, the value obtained by al - Khwarizmi is the more accurate.

Al-Biruni also wrote a treatise on time - keeping, wrote several treatises on the astrolabe and describes a mechanical calendar. He makes interesting observations on the velocity of light, stating that its velocity is immense compared with that of sound.