Mathematics

Al Kashi



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Al Kashi was a first class Islamic astronomer and mathematician.  He was born in the Persian town of Kashan in1380 AD and died forty nine years later in Samarkand.  During his career he worked with Ulugh Beg, the leading astronomer of the time. His collaborations with Ulugh Beg led to very accurate star tables, detailed texts on mathematics and a detailed knowledge of decimals and trigonometry.

During his youth Al Kashi was not able to develop his undoubted mathematical talents. At the time Persia experienced the deprivations of war and conquest the ruthless warlord, Tamurlane. Although Tamurlane forceably took skilled craftsmen from his conquered lands, especially Baghdad, and used them to found a great capital at Samarkand he had no interest in science and did not draw academics to his capital. The Al Kashi familywent un-noticed and lived in poverty throughout Tamerlane's reign.

The Al Kashi family fortunes changed when Tamurlane died in 1405. Tamurlane's son and heir, Sharrokh and his Persian wife, Goharshad appreciated science, culture and learning. They encouraged scholars to come to their court in Samarkand. When their  son, Ulugh Beg came to the throne in 1411 he took even more interest.  Ulugh Beg was not just a ruler, he was also an accomplished astronomer. .

When Al Kashi came to Samarkand in 1414 he came to a city where science was respected. In the years between 1417 and 1420 Ulugh Beg built a madrassah, or institute to encourage Islamic scholars to study in Samarkand.   Although over sixty mathematicians came to Samerkand Ulugh Beg though that only two were in the first division. Al Kashi and his colleage Qai Zada were the only mathematicans he would meet the challenges posed by Ulugh Beg.

When working as an astronomer, Al Kashi developed a highly accurate set of star table. He also published a treatise on the size and distance of the heavenly bodies and produced a treatise on the equipment that could be used for astronomical observation. Al Kashi knew how to calculate planetary alingments. He developed a gadget called the Plate of Conjunctions which could accurately determine the positions of the planets.,

Al Kashi was a close collaborator with Ulugh Beg so it is likely that some of his careful observations are included in Ulugh Beg's star tables.

As a mathematician Al-Kashi made some remarkable calculations. His work "The Key to Arithmetic" was published in 1425.  It displays a detailed knowledge of the decimal system and Pascal's triangle  His knowledge of decimals predates their use in the West by at lleast two hundred years.  His caculation of  Pi to 16 decimal places was not surpassed in accuracy until Ludolph van Ceulen published the value of the constant to 20 decimal places in 1594.

In a second work called "The Treatise on the Chord and Sine" Al Kashi demonstrated a detailed knowledge of trigonometry and cubic equations. The work includes a very accurate computation of sin 1 degree.  It also described an iterative method for solving cubic equations that was not rediscovered until many centuries later in the West.

In 1428 Ulugh Beg built a massive observatory at Samarkand which relied on a giant sextant to measure the angles to the stars. Al Kashi was closedly involved in its design and operation.  

Al Kashi spent almost his entire working life working on the problems of astronomy and mathematics at Samarkand. His life ended in 1429 in suspicious circumstances. He was working on "A Treatise on the Chord and Sine" at the time. There is a suspicion that he was murdered by Ulugh Beg although the motive and circumstances are not clear. 

The mathematical and astornomical achievements of Al Kashi place him far ahead of his rivals and reveal a level of knowledge not surpassed in the West for several centuries.

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