Q. & A. 711 to 1707 with solved Papers css 1971 to date

Abu Ali al-Hasan bin al-Hassan bin al-Haytham (Alhazen)
The renowned Arab mathematician and scientist Abu ’Ali alHassan bin al-Hassan al-Haytham was born at Basra, Iraq, in 965. Some time after he had achieved fame as a scholar he was induced to move to Cairo by the Fatimid Caliph al-Hakim, who died in 1021. Possibly the caliph, who is known to have patronized the great astronomer Ibn Yunus (died 1009), simply wished to add a luminary to his^court. According to one report, however, al-Hakim heard that Ibn al-Haytham had a plan for regulating the waters of the Nile and summoned the scholar to Cairo for the specific purpose of putting this plan into effect.
On his wa) to Aswan at the head of a group of workers, Ibn al-Haytham began to have doubts about his scheme. The ancient Egyptian buildings he observed on the banks of the Nile were so impressive that he realized that his plan, if it were at all feasible, would have been carried out by the capable engineers who had designed and built them. His fears were confirmed when he inspected the place to the south of Aswan called al-janadil. Here he had expected to see the water descend from a high ground, and he found that he had been mistaken. He now had to break the bad news to the caliph. His apology was accepted without penalty, and he was even put incharge of a government office.6
Ibn al-Haytham, however, did not feel safe in his new position, being as close to the eccentric and unpredictable al- Hakim, to be relived from his duties without appearing to be disloyal, he feigned madness until al-Hakim’s death. He then left the house to which he had been confined and moved to the Azhar Mosque, where he resumed his activities as an author and teacher of mathematics. According to one story, he earned his living by copying a number of
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basic mathematical works (including Euclid’s Elements and Ptolemy’s Almagest) once a year. He died in Cairo about 1040.
The preceding account, derived from a thirteenth century source, suggests that Ibn al-Haytham spent much of his later life in loneliness, either as a pretended madman or as a recluse leading an ascetic life in a qubbah (a small domed structure) at the gate of the Azhar Mosque. This impression is counterbalanced, however, by other scattered bits of information that indicate that he travelled a great deal and had contact with other well-known scholars of his time. He tutored the young prince al-Mubushir bin Fatik (died about

1060) in mathematics and astronomy and exchanged ”questions on the Milky Way and on place” with the Egyptian physician Ibn Ridwan(died 1061).

Two lists of Ibn al-Haytham’s works that were compiled by the author himself have been preserved by Ibn Abu Usaybi’ah (died

1270). The first list, written when Ibn al-Haytham was sixty-three, contains twenty-five title on mathematics and forty-five titles on physical and metaphysical questions. These works include discussions of Euclid, Apollonius, and Archimedes, as well as commentaries on the philosophical works of Aristotle and on the medical works of Galen. Some are devoted to questions of Islamic theology. The second list, written seventeen months after the first, contains twenty one titles covering roughly the same range of subjects as the first. More than sixty works of Ibn al- Haytham are now known to be extant, and most of them are included in a third list, which also was preserved by Ibn Abi Usaybi’ah.

Ibn al-Haytham’s most important contributions were in the fields of optics, astronomy, and mathematics. His most important single work is the comprehensive book, Kitab ai-Manazir (On Optics). Until the revival of optical research in Persia towards the end of the thirteenth century, Ibn al-Haytham was mainly known to the Islamic world as a mathematician and as an astronomer, but his best-known and most influential work in Europe was the Optics. It was largely on the basis of this book that George Sarton described Ibn ai- Haytham as ”the greatest Muslim physicist and one of the greatest students of optics of all times.
Other extant works by Ibn al-Haytham on optical subjects include ”On the Light of the Moon,” which argues that the moon shines like a self-luminous object though its light is borrowed from the sun. On the Halo and the Rainbow; ”On Spherical Burning
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Mirrors;” ”On Paraboloidal Burning Mirrors;” ”On the Burning Sphere;” and On the Shape of the Eclipse, which examines the camera obscura phenomena.
Although Ibn al-Haytham’s achievements in astronomy do not equal those of the best astronomers in Islam, his extant works show that he had mastered the techniques of Ptolemaic astronomy. Some of these works also reveal his ability to deal in a more than ordinary way with the standard problems that received attention from Arabic astronomers (such as the problem of determining the qibla, the direction to be faced in prayers) A critique of Ptolemaic Planetary models as presented in Ptolemy’s Almagest and planetary hypothes is appears to have inspired research that led to their replacement by non-Ptolemaic arrangement in the thirteenth century Maragha and fourteenth-century Damascus. The only one of his astronomical treatises known to the medieval West was On the Configuration of the World, in which the Ptolemaic planetary theory is described in terms of transparent physical bodies whose combined motions produce the apparent motions of the planets. The treatise was translated several times into Hebrew and Latin and has been shown to have influenced Renaissance astronomers.
Ibn al-Haytham secured a ttotable place in the history of mathematics by his treatment of the problem now bearing is Latinized name, Alhazen. This problem is discussed in the mathematical sections of his Optics. More than twenty other mathematical treatises of his, have also survived. Some of these deal with Euclidian problems-- for example, solution of the difficulties in Euclid’s elements and commentary on the premises of Euclid’s elements. Others deal with quadrature problems--for example, ”On the Quadrature of the Circle” and ”On Limes.” (figures contained between the arcs of two circles). Still others are on properties of conic sections. There is also a long treatise on the methods of analysis and synthesis, with illustrative applications to geometry, astronomy, and music.
In a short and not very informative autobiographical note appended to his first bibliography, Ibn al-Haytham wrote that at an early age he was perplexed by the plurality of sects and beliefs. Convinced that the truth was one, he doubted them all. Later on. when he was more capable of rational thought, he made it his aim to seek the essence of truth.” After much stud> he came to the conclusion that ”truth could only be reached thiough opinions whose

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matter was sensible and whose form was rational.” Though this does not tell us a great deal, it is in keeping with what we know of Ibn alHaytham’s strikingly empirical approach, and it is consistent with his abiding interest in the mathematical sciences.