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Hasan Ibn al-Haytham, Latinized as Alhazen, was an Mesopotamian mathematician, astronomer, and physicist of the Islamic Golden Age.

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Hasan Ibn al-Haytham, Latinized as Alhazen, was an Mesopotamian mathematician, astronomer, and physicist of the Islamic Golden Age.

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Alhazen was a polymath, writing on philosophy, theology and medicine.

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Alhazen held a position with the title vizier in his native Basra, and made a name for himself on his knowledge of applied mathematics.

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Legend has it that Alhazen feigned madness and was kept under house arrest during this period.

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Alhazen continued to live in Cairo, in the neighborhood of the famous University of al-Azhar, and lived from the proceeds of his literary production until his death in c 1040.

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Alhazen attempted to resolve this by asserting that the eye would only perceive perpendicular rays from the object—for any one point on the eye, only the ray that reached it directly, without being refracted by any other part of the eye, would be perceived.

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Alhazen argued, using a physical analogy, that perpendicular rays were stronger than oblique rays: in the same way that a ball thrown directly at a board might break the board, whereas a ball thrown obliquely at the board would glance off, perpendicular rays were stronger than refracted rays, and it was only perpendicular rays which were perceived by the eye.

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Alhazen later asserted that other rays would be refracted through the eye and perceived as if perpendicular.

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Alhazen assumed ray of light was radiated from specific points on the surface.

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Alhazen showed through experiment that light travels in straight lines, and carried out various experiments with lenses, mirrors, refraction, and reflection.

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Alhazen studied the process of sight, the structure of the eye, image formation in the eye, and the visual system.

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Ian P Howard argued in a 1996 Perception article that Alhazen should be credited with many discoveries and theories previously attributed to Western Europeans writing centuries later.

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Alhazen wrote a description of vertical horopters 600 years before Aguilonius that is actually closer to the modern definition than Aguilonius's—and his work on binocular disparity was repeated by Panum in 1858.

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Alhazen maintained that the rays that fell perpendicularly on the lens were further refracted outward as they left the glacial humor and the resulting image thus passed upright into the optic nerve at the back of the eye.

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Alhazen followed Galen in believing that the lens was the receptive organ of sight, although some of his work hints that he thought the retina was involved.

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Alhazen used his result on sums of integral powers to perform what would now be called an integration, where the formulas for the sums of integral squares and fourth powers allowed him to calculate the volume of a paraboloid.

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Alhazen eventually solved the problem using conic sections and a geometric proof.

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Kitab al-Manazir describes several experimental observations that Alhazen made and how he used his results to explain certain optical phenomena using mechanical analogies.

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Alhazen conducted experiments with projectiles and concluded that only the impact of perpendicular projectiles on surfaces was forceful enough to make them penetrate, whereas surfaces tended to deflect oblique projectile strikes.

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Alhazen used this result to explain how intense, direct light hurts the eye, using a mechanical analogy: Alhazen associated 'strong' lights with perpendicular rays and 'weak' lights with oblique ones.

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Khaleefa has argued that Alhazen should be considered the "founder of psychophysics", a sub-discipline and precursor to modern psychology.

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Alhazen argued against Ptolemy's refraction theory, and defined the problem in terms of perceived, rather than real, enlargement.

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Alhazen said that judging the distance of an object depends on there being an uninterrupted sequence of intervening bodies between the object and the observer.

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Alhazen's writings were more widely available in the Middle Ages than those of these earlier authors, and that probably explains why Alhazen received the credit.

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Besides the Book of Optics, Alhazen wrote several other treatises on the same subject, including his Risala fi l-Daw' .

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Alhazen investigated the properties of luminance, the rainbow, eclipses, twilight, and moonlight.

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Alhazen discussed the physics of the celestial region in his Epitome of Astronomy, arguing that Ptolemaic models must be understood in terms of physical objects rather than abstract hypotheses—in other words that it should be possible to create physical models where none of the celestial bodies would collide with each other.

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Ptolemy himself acknowledged that his theories and configurations did not always agree with each other, arguing that this was not a problem provided it did not result in noticeable error, but Alhazen was particularly scathing in his criticism of the inherent contradictions in Ptolemy's works.

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Alhazen considered that some of the mathematical devices Ptolemy introduced into astronomy, especially the equant, failed to satisfy the physical requirement of uniform circular motion, and noted the absurdity of relating actual physical motions to imaginary mathematical points, lines and circles:.

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Alhazen believed there was a "true configuration" of the planets that Ptolemy had failed to grasp.

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Alhazen intended to complete and repair Ptolemy's system, not to replace it completely.

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Alhazen held that the criticism of existing theories—which dominated this book—holds a special place in the growth of scientific knowledge.

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Alhazen kept a geocentric universe and assumed that celestial motions are uniformly circular, which required the inclusion of epicycles to explain observed motion, but he managed to eliminate Ptolemy's equant.

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Alhazen wrote a total of twenty-five astronomical works, some concerning technical issues such as Exact Determination of the Meridian, a second group concerning accurate astronomical observation, a third group concerning various astronomical problems and questions such as the location of the Milky Way; Alhazen made the first systematic effort of evaluating the Milky Way's parallax, combining Ptolemy's data and his own.

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Alhazen concluded that the parallax is smaller than Lunar parallax, and the Milky way should be a celestial object.

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In mathematics, Alhazen built on the mathematical works of Euclid and Thabit ibn Qurra and worked on "the beginnings of the link between algebra and geometry".

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Alhazen developed a formula for summing the first 100 natural numbers, using a geometric proof to prove the formula.

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Alhazen explored what is known as the Euclidean parallel postulate, the fifth postulate in Euclid's Elements, using a proof by contradiction, and in effect introducing the concept of motion into geometry.

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Alhazen formulated the Lambert quadrilateral, which Boris Abramovich Rozenfeld names the "Ibn al-Haytham–Lambert quadrilateral".

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In elementary geometry, Alhazen attempted to solve the problem of squaring the circle using the area of lunes, but later gave up on the impossible task.

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Alhazen solved problems involving congruences using what is called Wilson's theorem.

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Alhazen discovered the sum formula for the fourth power, using a method that could be generally used to determine the sum for any integral power.

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Alhazen could find the integral formula for any polynomial without having developed a general formula.

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Alhazen wrote a Treatise on the Influence of Melodies on the Souls of Animals, although no copies have survived.

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Alhazen carried out a detailed scientific study of the annual inundation of the Nile River, and he drew plans for building a dam, at the site of the modern-day Aswan Dam.

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Alhazen discussed space perception and its epistemological implications in his Book of Optics.

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Alhazen was a Muslim and most sources report that he was a Sunni and a follower of the Ash'ari school.

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Alhazen wrote a work on Islamic theology in which he discussed prophethood and developed a system of philosophical criteria to discern its false claimants in his time.

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Alhazen wrote a treatise entitled Finding the Direction of Qibla by Calculation in which he discussed finding the Qibla, where prayers are directed towards, mathematically.

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Alhazen made significant contributions to optics, number theory, geometry, astronomy and natural philosophy.

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Alhazen made the observation that the ratio between the angle of incidence and refraction does not remain constant, and investigated the magnifying power of a lens.

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Meanwhile, in the Islamic world, Alhazen's work influenced Averroes' writings on optics, and his legacy was further advanced through the 'reforming' of his Optics by Persian scientist Kamal al-Din al-Farisi in the latter's Kitab Tanqih al-Manazir .

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Alhazen wrote as many as 200 books, although only 55 have survived.

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In episode 5, Bronowski remarked that in his view, Alhazen was "the one really original scientific mind that Arab culture produced", whose theory of optics was not improved on till the time of Newton and Leibniz.

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