# Essay/Term paper: Carl friedrich gauss

## Essay, term paper, research paper: Science

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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.

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*Browns Mills, New Jersey, United States*

*Browns Mills, New Jersey, United States*

*Frederick, Maryland, United States*

*Browns Mills, New Jersey, United States*