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Text Book NotesTitle 8@_PID_HLINKSAH.@http://www.geocities.com/RaiText Book Notes
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TopicHistorical AnecdotesSub TopicText Book Notes EulerSummaryA brief history on EulerAuthorsAaron KlineDateAugust 27, 2002Web Site HYPERLINK "http://numericalmethods.eng.usf.edu" http://numericalmethods.eng.usf.edu
Leonard Euler was born in Basle on April 15, 1707. His father, Pastor Paul Euler, was instructed in mathematics by James Bernoulli. At a young age, he instilled in Euler a strong foundation in mathematics.
When young Euler was old enough, he was sent to the University of Basle, where he stayed at his grandmother's house. His father had hopes that he would choose to study ministry, to follow in his and his older brother's footsteps.
Euler remained a devout Christian his entire life, but Euler's love was in math, and he took every opportunity to study it. It was not long until he was worthy to receive lessons from John Bernoulli. However short lived his lessons, due to the wishes of his father, Euler began the study of theology. Later, his father realized Euler's strong attachment to mathematics. He eventually allowed his son to pursue his own dreams.
By 1726, Euler had an article in print, on isochronous curves in a resisting medium. In 1727 he published an article on reciprocal trajectories and submitted an entry for the 1727 Grand Prize of the Paris Academy on the best arrangement of masts on a ship. He received second place.
Euler was offered a post at St. Petersburg Academy of Sciences, Russia, which would involve him in teaching applications of mathematics and mechanics to physiology. Euler was a little hesitant, until he learned that he would not be appointed to the chair of physics at Basle. He then accepted the offer. Euler left Basel on April 5, 1727. He traveled by boat down the Rhine, crossed the German states by post wagon, then by boat from Lbeck and arriving in St Petersburg on May 17, 1727.
Euler served as a medical lieutenant in the Russian navy from 1727 to 1730. While in St. Petersburg he lived with Daniel Bernoulli, son of John Bernoulli. Unhappy in Russia, Daniel would ask Euler to bring him tea, coffee, brandy, and other delicacies from Switzerland.
Euler became professor of physics at the academy in 1730. Since this allowed him to become a full member of the Academy, he was able to give up his Russian navy post. Daniel left St Petersburg to return to Basel in 1733, and Euler was appointed to take his place as senior chair of mathematics. Now with a higher income, in the same year Euler married Gesell from Switzerland, a daughter of a successful painter.
In 1735, due to high stress Euler was thrown into a life threatening fever. He had symptoms of eyestrain, which may have brought on the fever. In the end, the fever left Euler blind in one eye.
After eight years, in response to the King of Prussia, Euler quit St. Petersburg and went to Berlin, 1741. He was presented to the queen mother, a princess who enjoyed associating with illustrious men. However, she was never able to draw him into any substantial conversation. In frustration, she asked way he would not converse with her. He replied, "Madam, it is because I have just came from a country where every person who speaks is hanged."
In 1744, Euler obtained the prize for the best work on the theory of magnetism at the Academy of Sciences, Paris. The same year he was appointed Director of the Mathematical Classes of the academy.
In 1760, a Russian army marched through Brandenburg, and among other things, they pillaged a farm. The Russian general was shocked to find that the farm had belonged to Euler. He immediately repaired the damage and gave Euler a large reimbursement. The Empress Elizabeth also gave him four thousand florins.
Impressed with the sympathy that Russia gave him, and due to a sense of loyalty, Euler went back to St. Petersburg where he remained the rest of his life. However, he was forced to leave his son behind, who was devoted in helping his father with his work and publications.
In 1771, a fire broke out in St. Petersburg, which reached Euler's house. Peter Grimm, a friend, knowing the danger that his friend was in; ran into the house and brought Euler out on his shoulder. In the end, Euler lost most of his furniture and his library.
Shortly after the fire Euler had a cataract operation, restored his sight for a few days. However, Euler seemed to have failed to take necessary care of himself, and he became totally blind on July 17. With the help of his family and pupils, he was able to dictate all of his calculations and memories. This made it possible for him to publish his works, despite his misfortunes.
In 1783, while enjoying the company of one of his grandchildren, Euler died of a stroke. He was 79.
Biography:
"Archimedes," January 26, 2002, HYPERLINK "http://www.historychannel.com/" http://www.historychannel.com/
Kahaner, D., Moler, C., Nash, S., Numerical Methods and Software. New Jersey: Prentice-Hall, Inc., 1989. pp. 212-214.
Forbes, G.E. The Euler-Mayer Correspondence (1751-1755). New York: E.G. Forbes, 1971.
Connor, O', Robertson, J.J, "Leonard Euler", January 18, 2002,http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Euler.html
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Text Book NotesTitle 8@_PID_HLINKSAH.@http://www.geocities.com/RainForest/Vines/2977/gauss/g_bio.html1+http://www.historychannel.com/D%http://numericalmethods.eng.usf.edu/
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Text Book NotesTitle 8@_PID_HLINKSAH.@http://www.geocities.com/RainForest/Vines/2977/gauss/g_bio.html1+http://www.historychannel.com/D%http://numericalmethods.eng.usf.edu/ 1h/ =!"#$%GaussGaussGaussJohan Friedrich Carl Gauss was born on April 30, 1777, outside of Brunswick, Germany. He was the only child of his parents and had a brother a few years older than him from his father's earlier marriage.
Gauss faced many challenges in his youth being born in a poor and uneducated family. His father worked many stressful and unprofitable jobs, and was always striving to meet the family s basic needs. Sometime between the ages of three and four, all the contributions that Gauss made almost never happened. Young Gauss almost drowned in a nearby canal.
A few years after acquiring a house within the city limits, Gauss s world would be turned upside down. It was the French Revolution; the armies of France overtook Brunswick. Because of the war, the 1780s were a surreal time for Gauss; the thought of ever being successful seemed to be an unrealistic dream.
In 1784, despite the war, Gauss was able to start elementary school. He already possessed the ability to read and write and perform elementary math, and that too without the help of his parents. It was apparent that even at this early age, Gauss had the makings of a genius.
In 1788, Gauss left his parents after being admitted to secondary school, however the effects of the war limited the teaching abilities of the school. Still Gauss took full advantage of the school and the skills he learned proved useful in his future success.
From 1792-1795 Gauss attended school at the Collegium Carolinum, a new science-oriented academy. During his time his arithmetic genius increasingly became ever more apparent. As an example, he once found the square root in two different ways up to fifty decimal places by expansions and interpolations. He also formulated the principle of least squares, while searching for regularity in the distribution of prime numbers.
Gauss entered the University of Gttingen in 1795. While there he made many discoveries, most of which had already been discovered. Discouraged with mathematics and his lack of making any true discover, Gauss was on his way to becoming a philologist. That is until he made a discovery that declared him a mathematician. Gauss obtained conditions for constructibility of regular polygons and was able to announce that the regular 17-gon was constructible by ruler and compasses. It had been a millennium since any advancement had been made in this matter.
Between 1796-1800, Gauss s mathematical thinking matured tremendously. Mathematical ideas came to him so easily and frequently that he had trouble getting them all down on paper. In 1798, Gauss returned to Brunswick, where he lived alone and continued his intensive work.
In January 1801, an astronomer had briefly observed that the new planet named Ceres could not be located. During the rest of that year, astronomers tried with no luck to relocate it. In September of the same year, Gauss decided to take up the challenge. He applied both a more accurate orbit theory (based on an ellipse rather than the usual circular method) and improved numerical methods (based on least squares). By December, Ceres was soon found. This was regarded as an amazing feat, due the lack of information and the vast distance of the planet, especially since Gauss did not reveal his methods.
Many of Gauss s discoveries were not credited to Gauss. Gauss had high standards for his own work and would not publish his findings without extensive proofs. When he published his discovery of least squares, he was accused of stealing the idea. This was because between the time of his discovery and his publication, another mathematician had stumbled on the idea. Gauss never said that he had been using the method for some time.
On February 23, 1855 Gauss died in his sleep. He was 88. Gauss made tremendous contributions to many fields of math, science and astronomy. After his death, Gauss s notebook and unpublished works included work that would have taken scientists decades of work.
Bibliography:
Archimedes, January 26, 2002, HYPERLINK "http://www.historychannel.com/" http://www.historychannel.com/
Buhler, W.K., Gauss A Biographical Study. New York: Springer-Verlag New York Inc., 1981. pp. 5-11, 15-18, 39-48.
Gauss' Biography, January 21, 2002,
HYPERLINK "http://www.geocities.com/RainForest/Vines/2977/gauss/g_bio.html" http://www.geocities.com/RainForest/Vines/2977/gauss/g_bio.html
Kahaner, D., Moler, C, Nash, S., Numerical Methods and Software. New Jersey: Prentice-Hall, Inc., 1989. pp. 212-214.
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