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Posted by admin in History, Uncategorized on December 13th, 2012
Research on Hur Movement
– MANZOOR H. KURESHI, Karachi, Sindh
….The Hur movement (1930-43) is one of the most important chapters that has played most vital role in the history of Sindh. Therefore in order to asses its impact on the pre and post independence period of modern Sindh, not only the Hur movement but the reign of two alien powers (Talpurs and British) who governed it through 19th and almost half of 20th Century also required exhaustive analysis with an eye of impartiality.
The Talpurs were a Baloach tribe from Baluchistan , soldiering in the native Kalhoras armed forces. After overthrowing their masters (1783), Talpurs turned Sindh as their personal fief which they divided into various branches of their families. Their triarchy ruled in a fashion of laissez-faire medieval monarchs, more engrossed in hunting than providing rule of law to the populace. Almost all fertile lands were either converted into royal hunting meadows or doled out to loyal clans serving in the state army. During their rule the condition of masses in general was extremely miserable to say the least.
When British conquered Sindh (1843), they brought with them various new concepts and enlightened ideas of welfare state already applied in Europe since 18th Century. They introduced modern education, latest system of administration and justice; revenue and communication; concept of planned cities on the basis of which they built Karachi post city. They not only developed roads and extensive railway infrastructure in shortest possible time, linking remotest places with main cities but also built Lloyd Barrage (1932), World’s greatest irrigation system. The lands of Sindh which were mostly dependent on seasonal rainfall, overflow of non-perennial Indus or few small size canals, now provided with network of Canals irrigating about 5 millions of acres hitherto virgin lands. Even credit of developing alphabets of modern Sindhi language goes to Sir Henry Bartle Edward Frere, then Commissioner of Sindh (1857). The institutions and infrastructure built by the British in 19th and beginning of 20th Century; were so sturdy and effective that despite total apathy shown to them subsequently are still catering to the needs of people.
The Hur revolt started during the middle of colonial period. Although this period was more benevolent, especially after East India Company was replaced by Crown (1858), which not only transformed the disposition of Sindh from medieval to modern but at the same time witnessed hectic developmental activities, carried out by the administration for the general welfare of public. This aspect needs to be analyzed.
Whereas upshot of Hur Movement was martial law imposed on lower Sindh and shifting of thousands non local ex-servicemen and Mari and Bugti tribal families who were given incentives by allotting to them thousands of acres fertile lands in Nara valley and reclaimed forest lands of ‘Mukhi forest’ hotbed of stiff resistance, as a permanent settlement. This policy changed the socio-political milieu as well as demography of Sindh forever… The colossal damage; socio-economically as well as politically, caused to the people of Sindh in the long run an outcome of confrontation with a far superior adversary; the British Empire also need to be examined by the scholars, when Hur Movement is made subject to in-depth research.
Courtesy: The Letters to the Editor, Daily Dawn Karachi
Posted by admin in History, India, Uncategorized on December 10th, 2012
Objective of the author
The objective behind writing this article is to acquaint the citizens of India with their national leaders and show how a dynasty has misused the democracy of this country. Several prestigious national assets and schemes are named after these lose-character people to immortalize them. Many other shocking facts are not presented in this article because of lack of supporting evidence.
The Early Years with Feroze Khan and the lonely Indira
Intellectual Indira was admitted in Oxford University but driven out from there for non-performance. She was then admitted to Shantiniketan University but, Guru Dev Rabindranath Tagore chased her out for bad conduct.
After driven out of Shantiniketan, Indira became lonely as father was busy with politics and mother was dieing of tuberculosis in Switzerland. Playing with her loneliness, Feroze Khan, son of a grocer named Nawab Khan who supplied wines etc to Motilal Nehru’s household in Allahabad, was able to draw close to her. The then Governor of Maharashtra, Dr. Shriprakash warned Nehru, that Indira was having an illicit relation with Feroze Khan. Feroze Khan was then in England and he was quite sympathetic to Indira. Soon enough she changed her
religion, became a Muslim woman and married Feroze Khan in a London mosque. Indira Priyadarshini Nehru changed her name to Maimuna Begum.Her mother Kamala Nehru was totally against that marriage. Nehru was not happy as conversion to Muslim will jeopardize her prospect of becoming Prime Minister.
Fool all of the People, all of the Times
So, Nehru asked the young man Feroze Khan to change his surname from
Khan to Gandhi. It had nothing to do with change of religion from Islam to Hinduism. It was just a case of a change of name by an affidavit. And so Feroze Khan became Feroze Gandhi, though it is an inconsistent name like Bismillah Sarma. Both changed their names to fool the public of India. When they returned to India, a mock vedic marriage was instituted for public consumption. Thus, Indira and her descendants got the fancy name Gandhi. Both Nehru and Gandhi are fancy names. As a chameleon changes its colour, this dynasty have been changing its name to hide its real identity.
Sanjay’s Shenanigans
Indira Gandhi had two sons namely Rajiv Gandhi and Sanjay Gandhi. Sanjay was originally named as Sanjiv that rhymed with Rajiv, his elder brother’s name. Sanjiv was arrested by the British police for a car theft in the UK and his passport was seized. On Indira Gandhi’s direction, the then Indian Ambassador to UK, Krishna Menon misusing his power, changed his name to Sanjay and procured a new passport.
The Nehru Dynasty Scion Sanjay Gandhi
Thus Sanjiv Gandhi came to be known as Sanjay Gandhi.
It is a known fact that after Rajiv’s birth, Indira Gandhi and Feroze Gandhi lived separately, but they were not divorced. The book “The Nehru Dynasty” (ISBN 10:8186092005) by K. N. Rao states that the second son of Indira (or Mrs. Feroze Khan) known as Sanjay Gandhi was not the son ofFeroze Gandhi. He was the son of another Muslim gentleman named Mohammad Yunus.
Interestingly Sanjay Gandhi’s marriage with the Sikh girl Menaka took place in Mohammad Yunus’ house in New Delhi. Apparently Yunus was unhappy with the marriage as he wanted to get him married with a Muslim girl of his choice. It was Mohammad Yunus who cried the most
when Sanjay Gandhi died in plane crash.
In Yunus’ book, “Persons, Passions & Politics” (ISBN-10: 0706910176) one can discover that baby Sanjay was circumcised following Islamic custom.
It is a fact that Sanjay Gandhi used to constantly blackmail his
mother Indira Gandhi, with the secret of who his real father is. Sanjay exercised a deep emotional control over his mother, which he often misused. Indira Gandhi chose to ignore his misdeeds and he was indirectly controlling the Government.
When the news of Sanjay Gandhi’s death reached Indira Gandhi, her
first question was “Where are his keys and his wrist watch?”. Some deep secrets about the Nehru-Gandhi dynasty seems to be hidden in those objects. The plane accident was also mysterious. It was a new plane that nosedive to a crash and yet the plane did not explode upon impact. It happens when there is no fuel. But the flight register shows that the fuel tank was made full before take-off. Indira Gandhi using undue influence of PM’s office prohibited any inquiry from taking place. So, who is the suspect?
“The Life of Indira Nehru Gandhi” (ISBN: 9780007259304) by Katherine Frank
The book “The Life of Indira Nehru Gandhi” (ISBN: 9780007259304) by Katherine Frank sheds light on some of Indira Gandhi’s other love affairs. It is written that Indira’s first love was with her German teacher at Shantiniketan. Later she had affair with M. O. Mathai (father’s secretary), then DhirendraBrahmachari (her yoga teacher) and at last with Dinesh Singh (Foreign Minister).
Amb. Natwar Singh-Witness
Former Foreign Minister K Natwar Singh made an interesting revelation about Indira Gandhi’s affinity to the Mughals in his book “Profile and Letters” (ISBN: 8129102358). It states that- In 1968 Indira Gandhi as the Prime Minister of India went on an official visit to Afghanistan. Natwar Sing accompanied her as an IFS officer in duty. After having completed the day’s long engagements, Indira Gandhi wanted to go out for a ride in the evening. After going a long distance in the car, Indira Gandhi wanted to visit Babur’s burial
place, though this was not included in the itinerary. The Afghan security officials tried to dissuade her, but she was adamant. In the end she went to that burial place. It was a deserted place. She went before Babur’s grave, stood there for a few minutes with head bent down in reverence. Natwar Singh stood behind her. When Indira had finished her prayers, she turned back and told Singh “Today we have
had our brush with history.” Worth to mention that Babur was the founder ofMughal rule in India, from which the Nehru-Gandhi dynasty have descended.
College Drop-out Rajiv Gandhi’s Moghul Dreams
It is difficult to count how many institutes of higher education are named after Rajiv Gandhi but, Rajiv Gandhi himself was a person of low calibre. From 1962 to 1965, he was enrolled for a Mechanical Engineering course at Trinity College, Cambridge. But, he left Cambridge without a degree because, he could not pass exams. Next year in 1966, he joined Imperial College, London but, again left it without a degree.
K. N. Rao in the above said book alleges that Rajiv Gandhi became a Catholic to marry Sania Maino. Rajiv became Roberto. His son’s name is Raul and daughter’s name is Bianca. Quite cleverly the same names are presented to the people of India as Rahul and Priyanka.
In personal conduct Rajiv was very much a Mughal. On 15th August, 1988 he thundered from the ramparts of the Red Fort: “Our endeavor should be to take the country to heights to which it belonged about 250-300 years ago. It was then the reign of Aurangzeb, the ‘jeziya’ master and number one temple destroyer.”
The press conference that Rajiv Gandhi gave in London after taking over as prime minister of India was very informative. In this press conference, Rajiv boasted that he is not a Hindu but a Parsi. Feroze Khan’s father and RajivGandhi’s paternal grandfather was a Muslim gentleman from the Junagarh area of Gujarat. This Muslim grocer by the name of Nawab Khan had married aParsi woman after converting her to Islam. This is the source where from the myth of Rajiv being a Parsi was derived. Mind that he had no Parsi ancestor at all. His paternal grandmother had turned Muslim after having abandoned the Parsi religion to marry Nawab Khan. Surprisingly, Parsi Rajiv Gandhi was cremated as per Vedic rites in full view of Indian public.
High School Graduate Antonia Maino a.k.a Sonia Gandhi, daughter of an Italian Fascist
Dr. Subramanian Swamy writes that Sonia Gandhi’s name was Antonia Maino. Her father was a mason. He was an activist of the notorious fascist regime of Italy and he served five years imprisonment in Russia. Sonia Gandhi have not studied beyond high school. She learnt some English from a English teaching shop named Lennox School at the Cambridge University campus. From this fact she boasts of having studied at the prestigious Cambridge University. After learning some English, she was a waitress at a restaurant in Cambridge town.
Sonia Gandhi had intense friendship with Madhavrao Scindia in the UK, which continued even after her marriage. One night at 2 AM in 1982, Madhavrao Scindia and Sonia Gandhi were caught alone together when their car met an accident near IIT Delhi main gate.
When Indira Gandhi and Rajiv Gandhi were Prime Ministers, PM’s security used to go to New Delhi and Chennai international airports to send crates of Indian treasures like temple sculptures, antiques, paintings etc to Rome. Arjun Singhas CM and later as Union Minister in charge of Culture used to organize the plunder. Unchecked by customs, they were transported to Italy to be sold in two shops named Etnica &Ganpati, owned by Sonia Gandhi’s sister Alessandra Maino Vinci.
Indira Gandhi died not because her heart or brain were pierced by bullets, but she died of loss of blood. After Indira Gandhi was fired upon, Sonia Gandhi strangely insisted that bleeding Indira Gandhi should be taken to Dr. Ram Manohar Lohia Hospital, in opposite direction to AIIMS which had a contingency protocol to precisely deal with such events. After reaching Dr. Ram Manohar Lohia Hospital, Sonia Gandhi changed her mind and demand that Indira Gandhi should be taken to AIIMS, thus wasting 24 valuable minutes. It is doubtful whether it was immaturity of Sonia Gandhi or a trick to speedily bring her husband to power.
Rajesh Pilot and Madhav Rao Scindia were strong contenders to the Prime Minister’s post and they were road blocks in Sonia Gandhi’s way to power. Both of them died in mysterious accidents.
There are circumstantial evidences pointing to the prima facie possibility that the Maino family have contracted LTTE to kill Rajiv Gandhi. Nowadays, Sonia Gandhi is quite unabashed in having political alliance with those like MDMK,PMK and DMK who praise Rajiv Gandhi’s killers. No Indian widow would ever do that. Such circumstances are many, and raise a doubt. An investigation into Sonia’s involvement in Rajiv’s assassination is necessary.
Dr. Subramanian Swamy’s book “Assassination Of Rajiv Gandhi — Unasked Questions and Unanswered Queries” (ISBN : 81-220-0591-8).
You may read Dr.Subramanian Swamy’s book “Assassination Of Rajiv Gandhi — Unasked Questions and Unanswered Queries” (ISBN : 81-220-0591-8). It contains indications of such conspiracy.
Sonia Gandhi, Rahul, and Priyanka- Italian Citizenship : How many Pakistani politicians have dual citizenship?
In 1992, Sonia Gandhi revived her citizenship of Italy under Article 17 of the Italian Citizenship Law. Under Italian law, Rahul and Priyanka are Italian citizens because Sonia was an Italian citizen when she gave birth to them.Rahul Gandhi’s Italian is better than his Hindi. Rahul Gandhi is an Italian citizen is relevant from the fact that on 27th September 2001 he was detained by the FBI at Boston airport, USA for traveling on an Italian passport. If a law is made in
India that important posts like that of President and Prime Minister should not be held by a person of foreign origin, then Rahul Gandhi automatically disqualifies to contend for the post of Prime Minister.
Rahul Gandhi, a Bilawal Bhutto type party animal or “Munna Bhai, MBBS”
After finishing school education, Rahul Gandhi got admission at the St. Stephens College in New Delhi, not on merit basis but on sports quota of rifle shooting. After a brief stay there in 1989-90, he did his BA from Rollins College, Florida in 1994. Just for doing BA one need not go to the US. The very next year, in 1995 he got M.Phil., degree from Trinity College, Cambridge. The genuineness of this degree is questioned as he has done M.Phil. without doing MA. Amaratya Sen’shelping hand is thought to be behind. Many of you might have seen thefamous movie “Munna Bhai MBBS”.
High Life and Hypocrisy of Gandhi Dynasty : India’s poor can eat cake!
In 2008 Rahul Gandhi was prevented from using an auditorium of the ChandraShekhar Azad University in Kanpur for a students’ rally. Subsequently, the Vice-Chancellor of the university, V.K. Suri, was ousted by the UP Governor. During 26/11 when the whole country was tense about how to tackle the Mumbai terror, Rahul Gandhi was lavishly partying with his friends till 5 AM. Rahul Gandhi advises austerity for all Congress members. He says it is the duty of all politicians to
be austere. On the other hand he has a ministerial bungalow with a fully equipped gym. He is a regular member of at least two of the Delhi’s poshest gyms, one of which is 5-star rated. Rahul Gandhi’s trip to Chennai in 2009 to campaign for austerity cost the party more than Rs 1 Crore. Such inconsistencies show that initiatives taken by Rahul Gandhi are not his own but, workout of his party men only.
Heritage of Sexual Escapades continue: Rahul Gandhi’s Live-in Girl Friend Veronica
During the 2007 election campaign in Uttar Pradesh, Rahul Gandhi said that “if anyone from the Nehru-Gandhi family had been active in politics then, the Babri Masjid would not have fallen”. It doubtlessly shows his Mohammedan affiliation as a loyalty to his ancestors. On Dec 31, 2004, John M. Itty, a retired college professor in Alappuzha district of Kerala, contended that action should be taken against
Rahul Gandhi and his girlfriend Juvenitta alias Veronica for staying together for three days at a resort in Kerela. It is a criminal offense under Immoral Trafficking Act as they are not married. Anyway, one more foreigner daughter-in-law is waiting to rule the tolerant Indians.
Sonia and Rahul Gandhi’s US $2 Billion in Swiss Banks
The Swiss magazine Schweizer Illustrierte’s 11th November 1991 issue revealed that Rahul Gandhi was the beneficiary of accounts worth US $2 billion controlled by his mother Sonia Gandhi. A report from the Swiss Banking Association in 2006 revealed that the combined deposits of Indian citizens are far greater than any other nation, a total of US $1.4 trillion, a figure exceeding the GDP of India. This dynasty rules greater than half of India. Ignoring the center, out of 28 states and 7 union territories, more than half of them have Congress government at any point of time. UptoRajiv Gandhi there was Mughal rule in India, with Sonia Gandhi, the Rome rule on India have started.
Recent research paints a new picture of the debt that we owe to Arabic/Islamic mathematics. Certainly many of the ideas which were previously thought to have been brilliant new conceptions due to European mathematicians of the sixteenth, seventeenth and eighteenth centuries are now known to have been developed by Arabic/Islamic mathematicians around four centuries earlier. In many respects the mathematics studied today is far closer in style to that of the Arabic/Islamic contribution than to that of the Greeks.
There is a widely held view that, after a brilliant period for mathematics when the Greeks laid the foundations for modern mathematics, there was a period of stagnation before the Europeans took over where the Greeks left off at the beginning of the sixteenth century. The common perception of the period of 1000 years or so between the ancient Greeks and the European Renaissance is that little happened in the world of mathematics except that some Arabic translations of Greek texts were made which preserved the Greek learning so that it was available to the Europeans at the beginning of the sixteenth century.
That such views should be generally held is of no surprise. Many leading historians of mathematics have contributed to the perception by either omitting any mention of Arabic/Islamic mathematics in the historical development of the subject or with statements such as that made by Duhem in [3]:-
… Arabic science only reproduced the teachings received from Greek science.
Before we proceed it is worth trying to define the period that this article covers and give an overall description to cover the mathematicians who contributed. The period we cover is easy to describe: it stretches from the end of the eighth century to about the middle of the fifteenth century. Giving a description to cover the mathematicians who contributed, however, is much harder. The works [6] and [17] are on “Islamic mathematics”, similar to [1] which uses the title the “Muslim contribution to mathematics”. Other authors try the description “Arabic mathematics”, see for example [10] and [11]. However, certainly not all the mathematicians we wish to include were Muslims; some were Jews, some Christians, some of other faiths. Nor were all these mathematicians Arabs, but for convenience we will call our topic “Arab mathematics”.
The regions from which the “Arab mathematicians” came was centred on Iran/Iraq but varied with military conquest during the period. At its greatest extent it stretched to the west through Turkey and North Africa to include most of Spain, and to the east as far as the borders of China.
The background to the mathematical developments which began in Baghdad around 800 is not well understood. Certainly there was an important influence which came from the Hindu mathematicians whose earlier development of the decimal system and numerals was important. There began a remarkable period of mathematical progress with al-Khwarizmi‘s work and the translations of Greek texts.
This period begins under the Caliph Harun al-Rashid, the fifth Caliph of the Abbasid dynasty, whose reign began in 786. He encouraged scholarship and the first translations of Greek texts into Arabic, such as Euclid‘s Elements by al-Hajjaj, were made during al-Rashid’s reign. The next Caliph, al-Ma’mun, encouraged learning even more strongly than his father al-Rashid, and he set up the House of Wisdom in Baghdad which became the centre for both the work of translating and of of research. Al-Kindi (born 801) and the three Banu Musa brothers worked there, as did the famous translator Hunayn ibn Ishaq.
We should emphasise that the translations into Arabic at this time were made by scientists and mathematicians such as those named above, not by language experts ignorant of mathematics, and the need for the translations was stimulated by the most advanced research of the time. It is important to realise that the translating was not done for its own sake, but was done as part of the current research effort. The most important Greek mathematical texts which were translated are listed in [17]:-
Of Euclid‘s works, the Elements, the Data, the Optics, the Phaenomena, and On Divisions were translated. Of Archimedes‘ works only two – Sphere and Cylinder and Measurement of the Circle – are known to have been translated, but these were sufficient to stimulate independent researches from the 9th to the 15th century. On the other hand, virtually all of Apollonius‘s works were translated, and of Diophantus and Menelaus one book each, the Arithmetica and the Sphaerica, respectively, were translated into Arabic. Finally, the translation of Ptolemy‘s Almagest furnished important astronomical material.
The more minor Greek mathematical texts which were translated are also given in [17]:-
… Diocles‘ treatise on mirrors, Theodosius‘s Spherics, Pappus‘s work on mechanics, Ptolemy‘s Planisphaerium, and Hypsicles‘ treatises on regular polyhedra (the so-called Books XIV and XV of Euclid‘s Elements) …
Perhaps one of the most significant advances made by Arabic mathematics began at this time with the work of al-Khwarizmi, namely the beginnings of algebra. It is important to understand just how significant this new idea was. It was a revolutionary move away from the Greek concept of mathematics which was essentially geometry.
Algebra was a unifying theory which allowed rational numbers, irrational numbers, geometrical magnitudes, etc., to all be treated as “algebraic objects”. It gave mathematics a whole new development path so much broader in concept to that which had existed before, and provided a vehicle for future development of the subject. Another important aspect of the introduction of algebraic ideas was that it allowed mathematics to be applied to itself in a way which had not happened before. As Rashed writes in [11] (see also [10]):-
Al-Khwarizmi‘s successors undertook a systematic application of arithmetic to algebra, algebra to arithmetic, both to trigonometry, algebra to the Euclidean theory of numbers, algebra to geometry, and geometry to algebra. This was how the creation of polynomial algebra, combinatorial analysis, numerical analysis, the numerical solution of equations, the new elementary theory of numbers, and the geometric construction of equations arose.
Let us follow the development of algebra for a moment and look at al-Khwarizmi‘s successors. About forty years after al-Khwarizmi is the work of al-Mahani (born 820), who conceived the idea of reducing geometrical problems such as duplicating the cube to problems in algebra. Abu Kamil (born 850) forms an important link in the development of algebra between al-Khwarizmi and al-Karaji. Despite not using symbols, but writing powers of x in words, he had begun to understand what we would write in symbols as xn.xm = xm+n. Let us remark that symbols did not appear in Arabic mathematics until much later. Ibn al-Banna and al-Qalasadi used symbols in the 15th century and, although we do not know exactly when their use began, we know that symbols were used at least a century before this.
Al-Karaji (born 953) is seen by many as the first person to completely free algebra from geometrical operations and to replace them with the arithmetical type of operations which are at the core of algebra today. He was first to define the monomials x, x2, x3, … and 1/x, 1/x2, 1/x3, … and to give rules for products of any two of these. He started a school of algebra which flourished for several hundreds of years. Al-Samawal, nearly 200 years later, was an important member of al-Karaji‘s school. Al-Samawal (born 1130) was the first to give the new topic of algebra a precise description when he wrote that it was concerned:-
… with operating on unknowns using all the arithmetical tools, in the same way as the arithmetician operates on the known.
Omar Khayyam (born 1048) gave a complete classification of cubic equations with geometric solutions found by means of intersecting conic sections. Khayyam also wrote that he hoped to give a full description of the algebraic solution of cubic equations in a later work [18]:-
If the opportunity arises and I can succeed, I shall give all these fourteen forms with all their branches and cases, and how to distinguish whatever is possible or impossible so that a paper, containing elements which are greatly useful in this art will be prepared.
Sharaf al-Din al-Tusi (born 1135), although almost exactly the same age as al-Samawal, does not follow the general development that came through al-Karaji‘s school of algebra but rather follows Khayyam‘s application of algebra to geometry. He wrote a treatise on cubic equations, which [11]:-
… represents an essential contribution to another algebra which aimed to study curves by means of equations, thus inaugurating the beginning of algebraic geometry.
Let us give other examples of the development of Arabic mathematics. Returning to the House of Wisdom in Baghdad in the 9th century, one mathematician who was educated there by the Banu Musa brothers was Thabit ibn Qurra(born 836). He made many contributions to mathematics, but let us consider for the moment consider his contributions to number theory. He discovered a beautiful theorem which allowed pairs of amicable numbers to be found, that is two numbers such that each is the sum of the proper divisors of the other. Al-Baghdadi (born 980) looked at a slight variant of Thabit ibn Qurra‘s theorem, while al-Haytham (born 965) seems to have been the first to attempt to classify all even perfect numbers (numbers equal to the sum of their proper divisors) as those of the form 2k-1(2k – 1) where 2k – 1 is prime.
Al-Haytham, is also the first person that we know to state Wilson’s theorem, namely that if p is prime then 1+(p-1)! is divisible by p. It is unclear whether he knew how to prove this result. It is called Wilson’s theorem because of a comment made by Waring in 1770 that John Wilson had noticed the result. There is no evidence that John Wilson knew how to prove it and most certainly Waring did not. Lagrange gave the first proof in 1771 and it should be noticed that it is more than 750 years after al-Haytham before number theory surpasses this achievement of Arabic mathematics.
Continuing the story of amicable numbers, from which we have taken a diversion, it is worth noting that they play a large role in Arabic mathematics. Al-Farisi (born 1260) gave a new proof of Thabit ibn Qurra‘s theorem, introducing important new ideas concerning factorisation and combinatorial methods. He also gave the pair of amicable numbers 17296, 18416 which have been attributed to Euler, but we know that these were known earlier than al-Farisi, perhaps even by Thabit ibn Qurra himself. Although outside our time range for Arabic mathematics in this article, it is worth noting that in the 17th century the Arabic mathematician Mohammed Baqir Yazdi gave the pair of amicable number 9,363,584 and 9,437,056 still many years before Euler‘s contribution.
Let us turn to the different systems of counting which were in use around the 10th century in Arabic countries. There were three different types of arithmetic used around this period and, by the end of the 10th century, authors such as al-Baghdadi were writing texts comparing the three systems.
1. Finger-reckoning arithmetic.
This system derived from counting on the fingers with the numerals written entirely in words; this finger-reckoning arithmetic was the system used by the business community. Mathematicians such as Abu’l-Wafa (born 940) wrote several treatises using this system. Abu’l-Wafa himself was an expert in the use of Indian numerals but these:-
… did not find application in business circles and among the population of the Eastern Caliphate for a long time.
Hence he wrote his text using finger-reckoning arithmetic since this was the system used by the business community.
2. Sexagesimal system.
The second of the three systems was the sexagesimal system, with numerals denoted by letters of the Arabic alphabet. It came originally from the Babylonians and was most frequently used by the Arabic mathematicians in astronomical work.
3. Indian numeral system.
The third system was the arithmetic of the Indian numerals and fractions with the decimal place-value system. The numerals used were taken over from India, but there was not a standard set of symbols. Different parts of the Arabic world used slightly different forms of the numerals. At first the Indian methods were used by the Arabs with a dust board. A dust board was needed because the methods required the moving of numbers around in the calculation and rubbing some out as the calculation proceeded. The dust board allowed this to be done in the same sort of way that one can use a blackboard, chalk and a blackboard eraser. However, al-Uqlidisi (born 920) showed how to modify the methods for pen and paper use. Al-Baghdadi also contributed to improvements in the decimal system.
It was this third system of calculating which allowed most of the advances in numerical methods by the Arabs. It allowed the extraction of roots by mathematicians such as Abu’l-Wafa and Omar Khayyam (born 1048). The discovery of the binomial theorem for integer exponents by al-Karaji (born 953) was a major factor in the development of numerical analysis based on the decimal system. Al-Kashi (born 1380) contributed to the development of decimal fractions not only for approximating algebraic numbers, but also for real numbers such as π. His contribution to decimal fractions is so major that for many years he was considered as their inventor. Although not the first to do so, al-Kashi gave an algorithm for calculating nth roots which is a special case of the methods given many centuries later by Ruffini and Horner.
Although the Arabic mathematicians are most famed for their work on algebra, number theory and number systems, they also made considerable contributions to geometry, trigonometry and mathematical astronomy. Ibrahim ibn Sinan(born 908), who introduced a method of integration more general than that of Archimedes, and al-Quhi (born 940) were leading figures in a revival and continuation of Greek higher geometry in the Islamic world. These mathematicians, and in particular al-Haytham, studied optics and investigated the optical properties of mirrors made from conic sections. Omar Khayyam combined the use of trigonometry and approximation theory to provide methods of solving algebraic equations by geometrical means.
Astronomy, time-keeping and geography provided other motivations for geometrical and trigonometrical research. For example Ibrahim ibn Sinan and his grandfather Thabit ibn Qurra both studied curves required in the construction of sundials. Abu’l-Wafa and Abu Nasr Mansur both applied spherical geometry to astronomy and also used formulas involving sin and tan. Al-Biruni (born 973) used the sin formula in both astronomy and in the calculation of longitudes and latitudes of many cities. Again both astronomy and geography motivated al-Biruni‘s extensive studies of projecting a hemisphere onto the plane.
Thabit ibn Qurra undertook both theoretical and observational work in astronomy. Al-Battani (born 850) made accurate observations which allowed him to improve on Ptolemy‘s data for the sun and the moon. Nasir al-Din al-Tusi (born 1201), like many other Arabic mathematicians, based his theoretical astronomy on Ptolemy‘s work but al-Tusi made the most significant development of Ptolemy‘s model of the planetary system up to the development of the heliocentric model in the time of Copernicus.
Many of the Arabic mathematicians produced tables of trigonometric functions as part of their studies of astronomy. These include Ulugh Beg (born 1393) and al-Kashi. The construction of astronomical instruments such as the astrolabe was also a speciality of the Arabs. Al-Mahani used an astrolabe while Ahmed (born 835), al-Khazin (born 900), Ibrahim ibn Sinan, al-Quhi, Abu Nasr Mansur (born 965), al-Biruni, and others, all wrote important treatises on the astrolabe.Sharaf al-Din al-Tusi (born 1201) invented the linear astrolabe. The importance of the Arabic mathematicians in the development of the astrolabe is described in [17]:-
The astrolabe, whose mathematical theory is based on the stereographic projection of the sphere, was invented in late antiquity, but its extensive development in Islam made it the pocket watch of the medievals. In its original form, it required a different plate of horizon coordinates for each latitude, but in the 11th century the Spanish Muslim astronomer az-Zarqallu invented a single plate that worked for all latitudes. Slightly earlier, astronomers in the East had experimented with plane projections of the sphere, and al-Biruni invented such a projection that could be used to produce a map of a hemisphere. The culminating masterpiece was the astrolabe of the Syrian Ibn ash-Shatir (1305-75), a mathematical tool that could be used to solve all the standard problems of spherical astronomy in five different ways.
References (21 books/articles)
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Article by: J J O’Connor and E F Robertson
Mr. Orya Maqbool Jan — Columnist, senior Journalist, expressed his desire for a country where people owned their culture, identity and language. He added that only technological and economic development could not ensure success. He said Pakistan should follow the example of Iran, a country that he said, had stuck to its language and culture and was all the better because of it. TEDxHUP International Conference was Organized by Hajvery University (HU) under license from TED, USA. It was held on Saturday, February 4 at the HU. The Conference brought together the Movers & Shakers of Pakistan as Keynote Speakers.The Theme of the Conference was — I Dream of a Pakistan.. You can view Videos of TEDx Talks by these remarkable speakers on www.TEDxHUP.com, and www.hup.edu.pk FOR MORE DETAILS ABOUT SUCH CONFERENCES, AND ATTENDING FUTURE CONFERENCES, VISIT WWW.HUP.EDU.PK Thank you for all the appreciation we received, it will inspire us to arrange even more remarkable events in future! =) Hajvery University (HU) w: www.hup.edu.pk e: [email protected] blog: hup.edu.pk/blog uan: 042- 111 777 007
This is the Office Channel of Hajvery University (HU). It helps you keep up with the news and events of HU, with regular entries of happenings, and events. For more detail visit HUP blog: www.hup.edu.pk/blog
Hajvery University From Wikipedia, the free encyclopedia Hajvery University Motto Motto in English Established Type Location Campus Colors Website
Kashf Al Mahjub[1]
Unveiling the Veiled
2002[2]
Private university
Lahore, Punjab, Pakistan
Urban/suburban
Red and blue
hup.edu.pk HU Main Entrance
Hajvery University (HU) is an institution of higher education in Lahore, Pakistan. HU is chartered by the government of Pakistan as an Autonomous Degree Awarding Institution.[3] The Higher Education Commission of Pakistan recognizes Hajvery University as a “category W” institution.[4]
Hajvery University has a main campus in the Industrial Area of Gulberg III, Lahore; a second campus (called the Euro Campus) near Gulberg III; a third campus under construction in Multan; and a fourth campus planned for Dubai.[5] The university has six constituent schools, each focused on a specific field of study: business; commerce and banking; engineering and computer science; fashion design; humanities and social sciences; and pharmacy.[6] The library at the main campus provides support for the courses offered with books, videos, journals and other reference sources.[5]
International relations
HU has international linkages and student/academic/staff exchange agreements with over 35 reputed universities from around world.[7] HU was a joint signatory of Erasmus Mundus 2009, 2010 Mobility Program. Some of the recent memorandums of understandings are with Istanbul Technical University (ITU)[8] and Ozyegin University, Istanbul.[9]
References
^ “Hajvery University Mission Statement”. Hajvery University. Retrieved 2010-08-16. ^ “Charter, Reputation & Accreditation”. Hajvery University. Retrieved 2010-08-16. ^ http://www.hup.edu.pk/features/charter-reputation-a-accreditation.html ^ “List of excluded universities in Pakistan”. Higher Education Commission of Pakistan. Retrieved 2010-08-16. ^ a b “The HU edge: Our Study Environment & Facilities”. Hajvery University. Retrieved 2010-08-16. ^ “Academics”. Hajvery University. Retrieved 2010-08-16. ^ Joint Signatory ^ HU & ITU MoU ^ HU OzU MoU HU Website