Essay/Term paper: Carl friedrich gauss

Essay, term paper, research paper:  Science

Carl Friedrich Gauss


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.
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.
In 1795, he continued his mathematical studies at the University of Gö
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.
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.
Barely 30 years old, already having made landmark discoveries in
geometry, algebra, and number theory Gauss was appointed director of the
Observatory at Göttingen. 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.
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
results he needed from statistics and differential geometry.
Most startling among the unpublished discoveries of Gauss is that of
non-Euclidean geometry. With a fellow student at Göttingen, he discussed
attempts to prove Euclid's parallel postulate -- Through a point outside of a
line, one and only one line exists which is parallel to the first line. As he
got closer to solving the postulate, the closer he was to non-Euclidean geometry,
and by 1824, he had concluded that it was possible to develop geometry based on
the denial of the postulate. He did not publish this work, conceivably due to
its controversial nature.
Another striking discovery was that of noncommutative algebras, which
has been known that Gauss had anticipated by many years but again failed to
publish his results.
In the 1820s, in collaboration with Wilhelm Weber, he explored many
areas of physics. He did extensive research on magnetism, and his applications
of mathematics to both magnetism and electricity are among his most important
works. He also carried out research in the field of optics, particularly in
systems of lenses. In addition, he worked with mechanics and acoustics which
enabled him to construct the first telegraph in 1833.
Scarcely a branch of mathematics or mathematical physics was untouched
by this remarkable scientist, and in whatever field he labored, he made
unprecedented discoveries. On the basis of his outstanding research in
mathematics, astronomy, geodesy, and physics, he was elected as a fellow in many
academies and learned societies. On February 23, 1855, Gauss died an honored and
much celebrated man for his accomplishments.