Carl Friedrich Gauss :: essays research papers

Carl Friedrich Gauss   Ã‚  Ã‚  Ã‚  Ã‚  Carl Friedrich Gauss was a German mathematician and scientist who dominated the mathematical community during and after his lifetime. His outstanding work includes the discovery of the method of least squares, the discovery of non-Euclidean geometry, and important contributions to the theory of numbers.   Ã‚  Ã‚  Ã‚  Ã‚  Born in Brunswick, Germany, on April 30, 1777, Johann Friedrich Carl Gauss showed early and unmistakable signs of being an extraordinary youth. As a child prodigy, he was self taught in the fields of reading and arithmetic. Recognizing his talent, his youthful studies were accelerated by the Duke of Brunswick in 1792 when he was provided with a stipend to allow him to pursue his education.   Ã‚  Ã‚  Ã‚  Ã‚  In 1795, he continued his mathematical studies at the University of Gà ¶ ttingen. In 1799, he obtained his doctorate in absentia from the University of Helmstedt, for providing the first reasonably complete proof of what is now called the fundamental theorem of algebra. He stated that: Any polynomial with real coefficients can be factored into the product of real linear and/or real quadratic factors.   Ã‚  Ã‚  Ã‚  Ã‚  At the age of 24, he published Disquisitiones arithmeticae, in which he formulated systematic and widely influential concepts and methods of number theory -- dealing with the relationships and properties of integers. This book set the pattern for many future research and won Gauss major recognition among mathematicians. Using number theory, Gauss proposed an algebraic solution to the geometric problem of creating a polygon of n sides. Gauss proved the possibility by constructing a regular 17 sided polygon into a circle using only a straight edge and compass.   Ã‚  Ã‚  Ã‚  Ã‚  Barely 30 years old, already having made landmark discoveries in geometry, algebra, and number theory Gauss was appointed director of the Observatory at Gà ¶ttingen. In 1801, Gauss turned his attention to astronomy and applied his computational skills to develop a technique for calculating orbital components for celestial bodies, including the asteroid Ceres. His methods, which he describes in his book Theoria Motus Corporum Coelestium, are still in use today. Although Gauss made valuable contributions to both theoretical and practical astronomy, his principle work was in mathematics, and mathematical physics.   Ã‚  Ã‚  Ã‚  Ã‚  About 1820 Gauss turned his attention to geodesy -- the mathematical determination of the shape and size of the Earth's surface -- to which he devoted much time in the theoretical studies and field work. In his research, he developed the heliotrope to secure more accurate measurements, and introduced the Gaussian error curve, or bell curve. To fulfill his sense of civil responsibility, Gauss undertook a geodetic survey of his country and did much of the field work himself. In his theoretical work on surveying, Gauss developed