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3:14 PM on February 06, 2009
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The history of mathematics is full of Arab inventions. The word 'algorithm', for example, comes from the name of the great mathematician Al-Khawarizmi, who is the father of algebra – another Arabic word, coming from the title of Al-Khawarizmi's work Kitab Al-Jabr (from jabara, 'to set bones'). The Arabs are also ultimately responsible for the fact that mathematicians the world over today use the letter 'x' to designate the unknown quantity – 'x' being the first letter of the Spanish word xay, which is a deformation of the Arabic shay, meaning simply 'thing'. In the golden age of Arab science, mathematical research was frequently carried out by great polymaths such as the poet Omar Khayyam, who in addition to penning his famous Quatrains also proposed solutions for equations of the third degree. But such research generally had a practical end in mind, such as calculating surface areas in order to assist in urban planning, for example. The study of astronomy was likewise encouraged with a view to practical ends, and more specifically with a view to predicting the future. On the basis of ancient Persian astrology, numerous Arab-Islamic scholars established longitudes, reformed the calendar, and went against Ptolemy's teachings by building a planetary model centred on the sun. Much later, Copernicus was in part inspired by their writings. The history of the word 'zero' is an informative tale. The Arabs borrowed their numerical system – which is far better adapted to arithmetic than the Roman system – from ancient India. When they did so, they named the '0' al-sifr, literally 'void'. The Arabic word was Latinised as cephirum and cifra, which in Italy was deformed to zefero, and then zero. It is the latter which passed into English and French as the name for the symbol indicating the absence of quantity or magnitude. At the same time, French borrowed the Medieval Latin word cifra, transforming it into chiffre ('number'), to designate numerical characters in general. It is from this same origin that English derived the word 'cipher', originally designating both 'nought' and '[any] Arabic numeral', before taking on its present-day meaning of 'code' (from the technique of transposing letters according to a numerical key).
In al-Uqlidisi's book Kita b al-fusul fi-l-hisab al-Hindii (The book of chapters on Hindu Arithmetic), two new contributions are significant: (1) an algorithm for multiplication on paper is given, and (2) decimal fractions are used for the first time. Both methods do not resemble modern ones, but the methods are easily understood using modern terminology.
Abu Kamil Shuja is sometimes known as al'Hasib and he worked on integer solutions of equations. He also gave the solution of a fourth degree equation and of a quadratic equations with irrational coefficients.
Abu'l-Wafa translated and wrote commentaries, since lost, on the works of Euclid, Diophantus and Al-Khwarizmi. For example, he translated Arithmetica by Diophantus. He is best known for the first use of the tangent function and compiling tables of sines and tangents at 15' intervals. This work was done as part of an investigation into the orbit of the Moon.
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11:03 PM on February 09, 2009
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