islamic astronomical and geographical observator,

The Persian mathematician Abu Rayhan al-Biruni, born in the year 973 in Khwarezm in the current Uzbekistan, spent his life traveling around Central Asia, make astronomical and geographical observations, studying and writing. Tolerant and eclectic personality, he learned many languages ​​and studied different cultures. As the largest part of his work dedicated to math subjects, astronomy and nearby areas (96 manuscripts a total of about 150 referenced, and 15 of the 22 who survived to this day), also wrote papers on medicine and pharmacology, metals and stones precious, religion and philosophy, and also a monumental history of India, who came to the present day, being translated into several languages. He worked until the end of his life and died in Ghazna, in today's Afghanistan, around 1050.

Al-Biruni was one of the most eminent figures of science and culture of the Islamic world in the centuries that followed the rapid expansion of the Muslim religion from the Arabian peninsula, through Central Asia to India, and North Africa to Iberia. Some key features of the cultural and scientific environment in which the Persian scientist stood out are probably familiar to many readers. I am thinking above all the idea that the Muslim world centuries VIII XV was the "bearer" or "transmitter" of great classical scientific traditions, particularly the fabulous Greek heritage, to the European Renaissance.

In the west of the modern age are often references to Islamic science as a mere translation and repetition of the classics. Renan, for example, wrote that "the Arab said Arab science has only the language (...) is not an Arab or even Muslim." Under this view, the Arab took account of scientific books while the European slept or thought other things.

This view reflects, beyond mere prejudices linked to historical circunstancialismos, a widespread attitude that is simply to say "I do not see does not exist."

In fact the great works of classical antiquity - such as Euclid, Archimedes, Apollonius, Diophantus, Ptolemy, etc. - They were translated, studied and commented by Islamic scientists. But to say only that is machine-washable. In the period in question flourished in the Islamic world a rich culture and in the case that interests us here, a science with original contributions in various fields of knowledge (especially in mathematics, astronomy and the like), and unrivaled for many centuries. This can be said though this scientific environment is not yet fully evaluated, not even in the contemporary Islamic world, where of course this historical reality is more well known. In the millennium after the eighth century are identified over a thousand active Islamic scientists. As sources are known thousands of scientific manuscripts and instruments, but many more remain still for analyzing, or even by catalog.

On the transfer of cultural and scientific heritage, you can set up an interesting parallel between the activity of translation of classics, especially Greek and Indian, sponsored by the caliphs of Baghdad in the eighth and ninth centuries, and the school of translators established in Toledo, under ecclesiastical and royal patronage in twelfth and thirteenth centuries. This school was created with the aim of achieving Latin versions, which came to have a lot of influence in Europe, the most important works of Arabic-speaking authors, whose names were often Latinized. In both cases there are cultures on the rise seeking dialogue with other established quality, and this meeting plays an important role the most universal of all languages, the language of science.

Several of the works translated from Arabic in Toledo were still ancient Greeks, which in some cases reached this only route to the Christian West. But many were original Islamic authors, and its importance is attested by the fact that some centuries later, have been printed in Europe.

*

In the narrow confines of this article, it is impossible to give an idea of ​​the abundance and diversity of the scientific contributions of the Islamic world. (Readers interested in mathematics can consult with profit chapter of Maria Fernanda Estrada in the recent history of mathematics published by the Open University.) So, I will refer only to some big names and topics treated.

An area where the Islamic contribution was notable was the study of equations, so that the chapter of mathematics that deals with it has a name of Arab origin, Algebra. The name derives from al-jabr, expression contained in the title of a work by Mohamed ibn Musa al-Khwarizmi (VIII-IX centuries). The means any thing as "reconstruction," and refers to the operation of adding the same amount to both members of the equation. This idea is present in an alternative sense of the word "algebraist" that the Iberian Peninsula has long synonymous time "rights". In Don Quijote, for example, is this excerpt concerning a character who had a party to the ribs fall off the horse, "En esto fueron razonando of them, hasta que un pueblo where the llegaron ventura fue un hallar algebraist, con quien to heal el Sansón desgraciado. "

The algebra book al-Khwarizmi was very influential - perhaps more than its intrinsic merit deserve - because of the practical use of the materials presented, in particular the 1st and 2nd degree equations solution, and rules for application in legacy issues , trade and accounting. At the same author should be a treaty, later translated into Latin, on the Indian numbering systems. Our words algorithm and digit derive from al-Khwarizmi's name. As for the symbols commonly used to designate the smallest natural numbers

0, 1, 2, 3, 4, 5, 6, 7, 8, 9

today we call them, with some historical impropriety, "Arabic numerals".

The arithmetic (or number theory, as today it is said) and algebra equations with their subjects were studied by Islamic mathematicians, with increasing detail and depth and surpassing the Greek heritage, over the following centuries. The decimal notation of numbers, and the practice of algorithms with them, they went generalizing. One of the big names on these issues is the mathematician and Persian poet Omar Khayyam (centuries XI-XII), with important studies on the extraction of roots and algebro-geometric investigations into the equations of the 3rd degree. When his name is also associated with famous formula, usually attributed to Newton, about sums of powers, whose beauty Fernando Pessoa / Alvaro de Campos dedicated a short poem.

Another area in which scientists of the Islamic world stood out was in trigonometry - that is, the study and calculation with angles and triangles - in the plane and on the ball. Investments in view were several, especially in the field of astronomy, geography and cartography. Some of the most important names in these themes are of al-Biruni and al-Battani (IX-X centuries), Latinized to Albatenius, author of important astronomical studies. In spherical trigonometry stood out also Jabir ibn Aflah (twelfth century), Seville, whose name was Latinized to Geber.

Even in mathematics, there is reference to pioneering studies of cryptography, the science of secure communications.

An integral part of Islamic scientific tradition in the period in question are the hundreds of instruments, astronomical and others who today are preserved. In addition to its scientific and technical sophistication, many of these instruments, such as spheres, sundials and astrolabes, are true works of art.

Arab astrolabe, Toledo - 1068

*

Not only in the mathematical sciences and related scientific contributions was relief by Islamic scholars. Among other names that could be mentioned, stand out al-Haytham (X-XI centuries), Latinized to Allacen, author of an influential treatise on optics, Jabir ibn Haiyan chemical (eighth century), also Latinized to Geber, and famous Persian physician-philosopher Abu Ali ibn Sina (X-XI centuries), Latinized to Avicenna, author of a Canon doctor who became reference text. With work mainly in philosophy, and huge impact on medieval Europe, it is compulsory to include Abu al-Walid ibn Rush (twelfth century), born in Cordoba and Latinized name to Averroes.

*

A substantial part of the activities of Islamic scientists in mathematics, geography and astronomy was related to religious themes: the development of the lunar calendar, the calculation of hours of prayer for astronomical methods, and determining, at each location, direction Holy Mecca, the qibla, necessary for prayers and for the guidance of the mosques. The latter problem is very interesting from a mathematical point of view.

The qibla in each location is defined by the direction of Mecca along the great circle arc joining the two points. If the earth were flat, the shortest line between two points would be a straight line and the problem would be very simple: once the coordinates of two points on a grid drawn on the plan, it immediately find the direction that goes from one to the other . But on a sphere we see that the issue is different and substantially more difficult, being necessary to use techniques of spherical trigonometry. In this issue dedicated Islamic scientists much attention, which explains to a large extent his interest in geometry of the sphere, but also the regular business of determining the geographical coordinates of numerous places in which again stood out al-Biruni.

Despite its religious motivation, the mathematical problem raised by determining the qibla is in the best interests elsewhere. For example, imagine that we are in Recife and want to navigate to Lisbon. We know the geographic coordinates of the starting point and the point of arrival. What direction should we follow? This problem at the outset of the trip, is exactly the same as determining the direction of Mecca. The differences arise because, unlike the situation of determining the qibla, which is static and, for each location, is resolved at once, here the problem is dynamic: if we, after we left the reef, always navigate in the same direction we calculated that the departure (using the compass to maintain steady course), do not turn to Lisbon. The mathematician who clarified this issue was the Portuguese Pedro Nunes (1502-1578), precisely in response to a question from a browser arrived in South America, the captain of the army, Brazil explorer and future governor of India Martim Afonso de Sousa. What Pedro Nunes showed was that a maximum arc (which is the direct route and shorter) is not a line of constant direction, and what it takes, traveling, always adjust the course - in a way that it explains - to reach the desired destination following the route of the great circle. Alternatively, you can follow a line of constant direction - to what is now called rhumb - from Recife to Lisbon, but this path is different from the direction that goes from one city to another along the great circle. This option is technically simpler (because determining the way forward is easy), but the journey is longer. Studies of Pedro Nunes had great influence on Europe's theory of navigation and cartography.

In its investigation of the rhumb line, Pedro Nunes cites several times the Sevillian Geber (Jabir ibn Aflah). Other works of Pedro Nunes, arguably the most notable Portuguese scientist of the sixteenth century, and even when there are references to various authors of Arabic.