Term Papers on Johann Carl Friedrich Gauss

Term Paper Title	Johann Carl Friedrich Gauss
# of Words	2022
# of Pages (250 words per page double spaced)	8.09

Johann Carl Friedrich Gauss

     Johann Carl Friedrich Gauss was a German mathematician, physicist and astronomer.
He is considered to be the greatest mathematician of his time, equal to the likes of
Archimedes and Isaac Newton.  He is frequently called the founder of modern
mathematics.  It must also be noted that his work in the fields of astronomy and physics
(especially the study of electromagnetism) is nearly as significant as that in mathematics.
He also contributed much to crystallography, optics, biostatistics and mechanics.
     Gauss was born in Braunschweig, or Brunswick, Duchy of Brunswick (now Germany)
on April 30, 1777 to a peasant couple.  There exists many anecdotes referring to his
extraordinary feats of mental computation.  It is said that as an old man, Gauss said
jokingly that he could count before he could talk.  Gauss began elementary school at the
age of seven, and his potential was noticed immediately.  He so impressed his teacher
Buttner, and his assistant, Martin Bartels, that they both convinced Gauss’s father that his
son should be permitted to study with a view toward entering a university.  Gauss’s
extraordinary achievement which caused this impression occurred when he demonstrated
his ability to sum the integers from 1 to 100 by spotting that the sum was 50 pairs of
numbers each pair summing 101.
     In 1788, Gauss began his education at the Gymnasium with the help of Buttner and
Bartels, where he distinguished himself in the ancient languages of High German and
Latin and mathematics.  At the age of 14 Gauss was presented to the duke of Brunswick -
Wolfenbuttel, at court where he was permitted to exhibit his computing skill.  His
abilities impressed the duke so much that the duke generously supported Gauss until the
duke’s death in 1806.  Gauss conceived almost all of his fundamental mathematical
discoveries between the ages of 14 and 17.  In 1791 he began to do totally new and
innovative work in mathematics.  With the stipend he received from the duke, Gauss
entered Brunswick Collegium Carolinum in 1792.  At the academy Gauss independently
discovered Bode’s law, the binomial theorem and the arithmetic-geometric mean, as well
as the law of quadratic reciprocity.  Between the years 1793-94, while still at the
academy, he did an intensive research in number theory, especially on prime numbers.
Gauss made this his life’s passion and is looked upon as its modern founder.  In 1795
Gauss left Brunswick to study at Gottingen University.  His teacher at the university was
Kaestner, whom Gauss often ridiculed.  His only known friend amongst the students
Farkas Bolyai.  They met in 1799 and corresponded with each other for many years.
     On March 30, 1796, Gauss discovered  that the regular heptadecagon, apolygon with
17 sides, is inscriptible in a circle, using only compasses and straightedge - - the first
such discovery in Euclidean construction in more than 2,000 years.  He not only
succeeded in proving this construction impossible, but he went on to give methods of
constructing figures with 17, 257, and 65,537 sides.  In doing so, he proved that the
constructions, with compass and ruler, of a regular polygon with an odd number of sides
was possible only when the number of sides was a prime number of the series 3,5 17, 257
and 65,537 or was a multiple of two or more of these numbers.  This discovery was to be
considered the most major advance in this field since the time of Greek mathematics and
was published as Section VII of Gauss’s famous work, Disquisitiones Arithmeticae.
With this discovery he gave up his intention to study languages and turned to
mathematics.
     Gauss left Gottingen in 1798 without a diploma.  He returned to Brunswick where he
received a degree in 1799.  The Duke of Brunswick requested that Gauss submit a
doctoral dissertation to the University of Helmstedt, with Pfaff chosen to be his advisor.
Gauss’s dissertation was a discussion of the fundamental theorem of algebra.  He
submitted proof that ever...

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