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mgf1107lecture29 - MGF 1107 EXPLORATIONS IN MATHEMATICS...

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MGF 1107 – EXPLORATIONS IN MATHEMATICS LECTURE 29 Henri Poincaré At the turn of the 20 th century, Henri Poincaré (1854-1912) was considered to be the finest living mathematician. One of the last to specialize in virtually every known branch of the subject, both pure and applied, he became a professor at the Sorbonne (Paris) in 1881, and wrote over 500 papers and 30 books. One of the famous problems he considered was the three-body problem . Newton’s laws of motion imply that to fully describe the motion of two bodies that interact solely with each other, for example a planet and its moon, we need to know the position and the velocity based on their initial values. There are six equations that need to be solved. A natural extension of Newton’s work was to try and determine what happens when there are three bodies that act upon each other due to gravity such as the sun, the earth, and the moon. However in this case we need to know the position and velocity of each body, and there are 18 equations to solve. The three-body problem was considered by many of the great mathematicians, including Euler who made substantial progress, but by 1887 a solution had still not been found.
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