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Sir Hamilton was an Irish mathematician who devised a non-commutative four-dimensional algebra of quaternions, or hypercomplex numbers. Their importance lay in their applications in geometry and mathematical physics, leading to vector theory. Hamilton grew up with his uncle who was a bit of an eccentric; for instance, he tied a string around young William's toe at night, ran it through a hole in the wall into his own bedroom, and then early each morning he would tug on the string to wake him and start him on his studies. By the age of 12, Hamilton was fluent in 10 languages and was appointed to a Mathematics Chair at the Royal Observatory in Dublin at a youthful age. One of Hamilton's successes was in proving that Newton's Equations and Lagrangian Mechanics were equivalent when the Lagrangian was the difference between the kinetic and potential energy of a system. Up to that time there were arguments over which was correct. He showed that they were different manifestations of the same thing. Hamilton tried to find a way to multiply points in three dimensions, in such a way as to allow division. The idea of using four dimensions instead, and the way to do it, came to him in a flash, as he walked with his wife by the Royal Canal. Since it is one of the few major mathematical discoveries which is precisely located in time and circumstances, the event is very well-known in the international mathematical community, and people from all over the world know Hamilton's Bridge. When he made the discovery, Hamilton paused under Brougham (or Broom) Bridge, took out his penknife, and scratched the fundamental formula i*i = j*j = k*k = i*j*k = -1 into the stone. The day was the 16 October 1843. No trace of this can be found today. Hamiltons own description: But on the 16th day of the same month - which happened to be a Monday, and a Council day of the Royal Irish Academy - I was walking in to attend and preside, and your mother was walking with me, along the Royal Canal, to which she had perhaps driven; and although she talked with me now and then, yet an under-current of thought was going on in my mind, which gave at last a result, whereof it is not too much to say that I felt at once the importance. An electric circuit seemed to close; and a spark flashed forth, the herald (as I foresaw, immediately) of many long years to come of definitely directed thought and work, by myself if spared, and at all events on the part of others, if I should even be allowed to live long enough distinctly to communicate the discovery. Nor could I resist the impulse - unphilosophical as it may have been - to cut with a knife on a stone of Brougham Bridge, as we passed it, the fundamental formula ... He also put some ideas of Fermat into a new perspective. Hamilton took Lagrange's action property and showed that the path a particle would take would be the path of least action. This correlation between the motion of waves (as light was understood at the time) and that of particles could be described in a common way, hints, in retrospect at least, to the wave-particle duality that we understand in modern quantum theory. Perhaps Hamilton's most important contribution came from his reformulation of Newton's Laws. In the same way that Lagrange provided a new method for solving mechanical problems, Hamilton put forward still another formalism. He showed that the results were equivalent in the three methods, but his proves to be most useful for a certain class of problems. The theory stems from a new variable called the Hamiltonian, which is the sum of the system's kinetic and potential energy. And the equations of motion derive from this. It turns out that Hamiltonian mechanics were the starting point for Schrödinger's development of his Wave Mechanics, the classical theory simply twisted to account for the quantum observations.
Haret the first Romanian doctor in mathematics at Paris, was born at Hanul Conachi, Putna. After graduating the high school, in 1869, Haret enlisted at the University of Bucharest, Faculty of sciences, section of physics-mathematics. On December 3, 1870, while student, Haret was appointed professor of mathematics with provisory title at the Central seminary Nifon from Bucharest. At that time the requirements for taking a position in the secondary education was only necessary the baccalaureate and a competition examination. Haret took his license in mathematics in Bucharest in 1874. In 1872 he resigned from the department of mathematics from Nifon. In 1874 Titu Maiorescu, minister of Public Education gave Haret, following a competition, a scholarship to study mathematics in Paris. At Paris, he took again the license in mathematics in August 1875 and the license in physical sciences, in July 1876. He passed the doctorate at Paris, Sorbona, on January 18/30 1878, with the thesis "Sur L'invariabilité des grands axes des orbites planétaires". He presented his thesis in front of a commission formed of Puiseux as president and Briot and Baillard, as members. Haret was thus our first doctor in mathematics at Paris. When he returned to the country, on April 1st 1878, the department of mechanics was separated of that of infinitesimal calculation, the first one being given as assistant to Haret, the second one remaining to Iacob Lahovary. On October 2, 1878 Haret was appointed assistant to the department of mechanics. He was the undisputed soul of the Romanian school between 1880 and 1910 and he was thus named the "Man of the school". As teacher, Spiru Haret taught at the University of Bucharest, the Faculty of sciences, section of physics - mathematics, rational mechanics, between 1878 and 1910. Haret was also appointed teacher for the preparative year at the School of Bridges and roads. Between 1885 - 1910 Haret only taught analytical geometry at the School of bridges and roads. Haret taught rational mechanics at the School of artillery and engineer officers between, 1881 - 1890. He died on December 17, 1912, of cancer, a few months after he made the eulogy to the great French scientist Henri Poincaré, at the Romanian Academy.
An area of Andalusian intellectual activity was philosophy, where an attempt was made to deal with intellectual problems posed by the introduction of Greek philosophy into the context of Islam. One of the first to deal with this was Ibn Hazm, who as the author of more than four hundred books has been described as "one of the giants of the intellectual history of Islam." Ibn Hazm of Cordova said that it was impossible to understand anything that can't expressed in language, language was instituted by Allah, therefore the only thing to be relied upon is the text itself of the Qur'an and of the Reports, taken in their straightforward sense. He influences among others with his ideas on logic the work of Lullus. For the interpretation of sacred texts, he put together a Zahiri grammar in which he specifically eliminates the ambiguities that grammarians were using to explain certain syntactical forms. He takes the position that language itself provides all that is necessary for the understanding of its content and that, therefore, God, who revealed the Qur'an in clear (mubin) Arabic, has used the language to say precisely what he means. Each verse should be understood grammatically and lexically in its immediate and general sense: when God wants a verse to have a specific meaning, he provides an indication (dalil), in the same verse or elsewhere, which allows the meaning to be restricted. As one of the most eminent theologians and jurists, Ibn Hazm, insisted that moral qualities were mandatory in a physician. A doctor, he wrote, should be kind, understanding, friendly, and able to endure insults and adverse criticism. Furthermore, he went on, a doctor should keep his hair and fingernails short, wear clean clothes, and behave with dignity.
Zhang Heng (78-139) was a Chinese mathematician searching for the value of pi. His use of the square root of 10 is one of the earliest approximations known. He was also the inventor of a primitive seismograph.
Born: 14 April 1629 in The Hague, Netherlands Died: 8 July 1695 in The Hague, Netherlands
Dutch physicist who was the leading proponent of the wave theory of Light, was also the mentor of Leibniz in math and mechanics. The most important of Huygens's work was his Horologium Oscillatorium published at Paris in 1673. The first chapter is devoted to pendulum clocks. The second chapter contains a complete account of the descent of heavy bodies under their own weights in a vacuum, either vertically down or on smooth curves. Amongst other propositions he shews that the cycloid is tautochronous. In the third chapter he defines evolutes and involutes, proves some of their more elementary properties, and illustrates his methods by finding the evolutes of the cycloid and the parabola. These are the earliest instances in which the envelope of a moving line was determined. In the fourth chapter he solves the problem of the compound pendulum, and shews that the centres of oscillation and suspension are interchangeable. In the fifth and last chapter he discusses again the theory of clocks, points out that if the bob of the pendulum were, by means of cycloidal clocks, made to oscillate in a cycloid the oscillations would be isochronous; and finishes by shewing that the centrifugal force on a body which moves around a circle of radius r with a uniform velocity v varies directly as v² and inversely as r. This work contains the first attempt to apply dynamics to bodies of finite size, and not merely to particles. Besides these works Huygens took part in most of the controversies and challenges which then played so large a part in the mathematical world, and wrote several minor tracts. In one of these he investigated the form and properties of the catenary. In another he stated in general terms the rule for finding maxima and minima of which Fermat had made use, and shewed that the subtangent of an algebraical curve f(x,y) = 0 was equal to y fy /fx , where fy is the derived function of f(x,y) regarded as a function of y. In some posthumous works, issued at Leyden in 1703, he further shewed how from the focal lengths of the component lenses the magnifying power of a telescope could be determined; and explained some of the phenomena connected with haloes and parhelia.
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