AL-KHOWARIZMI AND THE CONCEPT OF ZERO

Al Khowarizmi - Great Khwarazmian Mathematician -  Inventor of the loarithm algorithm and the usage of zero in mathematics and the word algebra originating  (الجبر al-jabr "restoration") from the title of his book Ilm al-jabr wa'l-muḳābala.

 

The Stamp from the  OJSC "Uzbekistan pochtasi" and put into circulation by the State Committee of Communication, Information and Communication Technologies of the Republic of Uzbekistan from April 10, 2014 as a standard postage stamp. 

 

 

The ancient Indians represented zero as a circle with a dot inside. In Sanskrit, it was called "soonya". This and the decimal number system fascinated zIslamic scholars who came to India. Al-Khowarizmi (790 AD - 850 AD) wrote Hisab-al-Jabr wa-al-Muqabala (Calculation of Integration and Equation) which made Indian numbers popular. "Soonya" became "al-sifr" or "sifr". The impact of this book can be judged by the fact that "al-jabr" became "Algebra" of today. An Italian Leonardo Fibonacci (1170 AD - 1230 AD) took this number system to Europe. The Arabic  "sifr" was called "zephirum" in Latin, and acquired many local names in Europe including "cypher". Today this system is called Hindu-Arabic System.  The positional system of representing integers revolutionised the   mathematical calculations and also helped in Astronomy and accurate  navigation. The use of positional system to indicate fractions was introduced around 1579 AD by Francois Viete. The dot for a decimal  point  came to be used a few years later, but did not become popular  until its  use by Napier. The binary system used in modern computing uses 1 and 0.

 

AL-BIRUNI, Abu Arrayhan Muhammad Ibn Ahmad

Abou Rayhan Mohamed Al Biruni (973-1048) was born at Kath in Khwarazm (now Beruni) located in the modern day Republic of Karakalpakstan (in Uzbekistan). He was an outstanding astronomer, astrologer, mathematician, physicist, physician, geographer, geologist, historian, and indefatigable traveller. Conversant in Turkish, Farsi, Sanskrit, Hebrew and Arabic and Hindi, he became the most important interpreter of Indian science to Islam. His many scientific achievements include: pioneering the notion that the speed of light is much greater than the speed of sound, disputing the European Ptolemaic view that Africa stretched infinitely to the South, insisting it was surrounded by water, advancing the controversial but correct view that the Indus valley was once a sea basin, and explaining natural springs by the laws of hydrostatics.

Al-Biruni studied with the renowned astronomer and mathematician Abu Nasr Mansur, a prince of the ruling Banu Iraq in Khwarezm. Al-Biruni’s knowledge of several languages allowed him to understand existing ideas and bring a fresh and original approach to his own work. At 17 he computed the latitude of Kath by observing the maximum altitude of the sun. By the time he was 21 in the year 994, he had written several short works. One that survived is Cartography, a work on map projections. He regularly corresponded with his contemporary, the famous physician Ibn Sina better known to the West as Avicenna, who reconciled Greek learning with Muslim thought with his translation of Euclid into Arabic.

At the end of the 10th century and the beginning of the 11th century there were numerous civil wars in the region where al-Biruni lived. In 995 the rule of the Banu Iraqi was overthrown in a coup that forced al-Biruni to flee but to where is not quite clear. Some theorize by analyzing his writings that he then went to the city of Rayy, near  present day Tehran, where he had no patron and lived in poverty. It is known he returned to his homeland by June 4, 1004, which then was ruled successively by brothers Ali ibn Ma’mun and Abu’l Abbas Ma’mun who provided generous support for al-Biruni’s scientific work. Here he described an eclipse of the moon from Jurjaniyya, (modern Kunya- Urgench, Turkmenistan) in collaboration with his teacher Abu Nasr Mansur, but at the cost of not being free to leave. He was to spend the next seven years in the court of Prince Khwarimshah Abou Al Abbas Ma’moum. In  1017 Sultan Mahmud of Ghazni (in Afghanistan) conquered Abu’l Abbas Ma’mum’s kingdom even though both Abu’l and his brother had married Mahmud’s sisters.

This political upheaval did not interfere with al-Biruni’s research. On the contrary, his scholarship so impressed Mahmud that he took the scholar with him on his military excursions in India. Over a period of 20 years he traveled all over the country, learning Hindu philosophy, mathematics, geography and religion from the Pandits, and in turn he taught them Greek and Arabic science and philosophy. His long stay allowed him to learn the Sanskrit which enabled him to make contact with the greatest scholars of this country exchanging with them his knowledge from the Baghdad school against that of India. Upon his return to Afghanistan, all the knowledge from his observations of his travels in India were recorded in his book Kitab al-Hind. In this work he mentions that he translated two Sanskrit books into Arabic. One, named Sakaya, which dealt with the creation of things and their types, and the second, Patanjal, examining what happens after the soul leaves the body.

On returning from India, al-Biruni settled in the court of Gazna (now in Afghanistan), with Sultan Massoud to whom he dedicated his third main work entitled Qanun-I Masoodi, a book in which he discusses several theorems of astronomy, trigonometry, solar, lunar, and planetary motions. That same year, Al Biruni composed his Kitab al tafhim li awa′il sina′at al tanjim (“Book of Instructions in the Elements of the Art of Astrology”), also known as the Tafhim. In this book he follows a logical progression from first principles, beginning with geometry, then arithmetic, astronomy, geography, chronology and a discussion of the astrolabe before reaching his introduction to astrology. He described the general characteristics of the “planets,” Saturn, Jupiter, Mars, the Sun, Venus, Mercury, and the Moon and describes their role in determining people’s actions and professions, their bodies and diseases, animals, vegetables & minerals. As an illustration, he claimed Saturn rules farming, grave-digging, captivity, fathers, slaves, wicked people, hair, skin, bones, old age, sickness, poverty, death, horses, olive trees, almonds, hard stones, lead, pepper, sleep, and poisons. These are only a small sampling of those things ruled by Saturn, and in a like manner the other six “planets” rule as many things.

Among his other books is the al-Athar al-Baqia in which he connects accounts of ancient histories of nations with known geographical facts. In it he also discusses whether or not the Earth rotates on its axis, and gives the correct longitudes and latitudes of several places. His treatise Kitab-al-Saidana contains the then existing Arabic knowledge of Indian medicine.

It is believed over his lifetime that al-Biruni wrote some 180  books and articles, with only about a fifth having survived. One of his most important texts is Shadows, which covers shadows, gnomonics, the history of the tangent and secant functions, applications of the shadow functions to the astrolabe, shadow observations for the solution of astronomical problems and for the fixing of times for Muslim prayers. In addition, al-Biruni gave a full description of the Hindu positional principle of numeration and proved Heron’s formula and Brahmagupta’s generalisation. In physics he studied specific gravity and the causes of artesian wells.

In Kitab-al-Jamahir, al-Biruni became the first to determine the hardness of minerals and their specific weights. He described the ratios between the densities of gold, mercury, lead, silver, bronze, copper, brass, iron and tin. He displayed his results as combinations of integers and numbers of the form 1/n, with n = 2, 3, 4,…, 10. He was the first to see gas-liquid inclusions in gems – ancient fluids that took part in the formation of mountain crystals, topaz, amethysts, sapphires, ambers, and other minerals. He was also an astrologer who astonished people with the accuracy of his predictions.

Al-Biruni died at the age of 75, having spent 40 years gathering knowledge and significantly contributing to science. He is said on his death bed to a former student  “Isn’t it better that I leave the world knowing the solution to this problem than leaving it without knowing ?” I then repeated the question to him and he gave me the solution he had previously promised me.  A few seconds later, the great scholar took his last breath”.

Source: http://www.robertnowlan.com/pdfs/al-Biruni,%20Muhammad.pdf (ED)

Qaraqalpag'im (Каракалпагым)

Максет Отемуратов (Каракалпакстан) - Каракалпагым (4:27)




Source http://vk.com/video-1327917_17626798