Gauss's Method

   , DEGAUSS

   Karl Friedrich Gauss (1777-1855), German mathematician and scientist, was one of the three greatest mathematicians of who ever lived, the others being Archimedes and Newton. (Of course, Gauss lived about a century before Albert Einstein.) Gauss's 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.

   At the age of three this mathematical genius called attention to some errors in his father's insurance fund bookkeeping. At ten he was able to sum up, independently, complex arithmetical series. At school he showed little of his precocious talent until age nine. The master set forth a series of numbers in arithmetical progression in what appeared to be a complicated problem. Although Gauss had never been taught the method for solving this problem, he turned in his slate within seconds. At the end of the period there was a pile of slates on top of Gauss's, all with incorrect answers. The master was stunned to see that Gauss had the correct answer. When he was not yet twenty-one years of age, and still a student at Gottingen, he established proof of the fundamental theorem of algebra, which had baffled mathematicians since Euclid's day.

   Gauss was not sure whether his major interest was philology or mathematics. He chose the latter in 1796 when he discovered how to construct a regular polygon of seventeen sides, using only a compass and a straightedge. By 1824 he had concluded that it was possible to develop geometry based on the denial of the postulate. Gauss developed the theory of elliptical functions.

   Gauss's greatest treatise, a book on the theory of numbers titled Disquisitiones arithmeticae, established his reputation in 1801. On January 1, 1801, Giuseppe Piazzi discovered the asteroid Ceres. After a short time, it was lost in the sun's rays. Recalling his method of least squares, Gauss computed the orbit of Ceres. At the end of the year, the asteroid was clearly seen in the position he had predicted. Gauss's method of computing orbits is still in use today.

   Gauss originated the Gauss curvature, the reciprocal of the product of the two principal radii of curvature of a surface at any of its points, and also the Gauss curve, a probability curve. He originated the Gaussian distribution, a theoretical frequency distribution used in statistics that is bell-shaped, symmetrical, and of infinite extent. The Gauss meter indicates the strength of a magnetic field at any point directly in gauss.

   Because of his brilliant mind, science can now wrestle successfully with the mathematical theory of electricity. Gauss was also responsible for studies of magnetism and electricity, and the measurement unit of magnetic induction. A magnetic unit in electricity is named for him. The German magnetic mines used during World War II took a heavy toll on British shipping. The magnetism of an approaching ship detonated the mines lying on the bottom of the sea. A countermeasure— neutralizing the ship's magnetic field—was created and was called degaussing.