Here is the synopsis of our sample research paper on Mathematician Leonhard Euler’s Refutation of Pierre de Fermat’s Conjecture
. Have the paper e-mailed to you 24/7/365.
Essay / Research Paper Abstract
This is a 3 page paper discussing Euler’s refutation of Fermat’s conjecture. In 1637, French lawyer Pierre de Fermat wrote that he had “discovered a truly marvelous proof which this margin is too narrow to contain” in regards to a mathematical statement which had been unproven for over 1000 years. The basis of Fermat’s (“Last”) theorem or conjecture began with that of the Pythagoras equation [x.sup.2] + [y.sup.2] = [z.sup.2] which he proved “had an infinite set of whole number solutions” which related to the lengths of the sides of a right-angled triangle. Pythagoras did not know “how many solutions existed if the exponent in his equation were a number greater than 2”. Fermat claimed that “for any exponent greater than 2, there were no solutions at all”. During his lifetime however, Fermat often did not supply “proofs” of many of his theorems but many mathematicians since his time have been able to prove his claims to be correct except for that in relation to the Pythagoras equation. Swiss mathematician Leonard Euler (1707-1783) did however work further on many of Fermat’s theorems and “later proved that there are no solutions when the exponent is 3” and “unfortunately, an infinite number of cases remained and the case-by-case method was doomed to fail”. While Fermat’s Last Theorem proved to be difficult to prove, Euler managed to disprove and refute other assertions such as “2^(2^n) = p, where p is a prime number” and found that it is only true for the first four cases provided by Fermat.
Bibliography lists 4 sources.
Page Count:
3 pages (~225 words per page)
File: D0_TJEuler1.rtf
Buy This Term Paper »
Unformatted sample text from the term paper:
a mathematical statement which had been unproven for over 1000 years. The basis of Fermats theorem or conjecture began with that of the Pythagoras equation [x.sup.2] + [y.sup.2] = [z.sup.2]
which he proved "had an infinite set of whole number solutions" which related to the lengths of the sides of a right-angled triangle (Levine, 1998, p. 1485). Pythagoras did not
know "how many solutions existed if the exponent in his equation were a number greater than 2". Fermat claimed that "for any exponent greater than 2, there were no solutions
at all" (Levine, 1998, p. 1485). During his lifetime however, Fermat often did not supply "proofs" of many of his theorems but many mathematicians since his time have been able
to prove his claims to be correct except for that in relation to the Pythagoras equation. Swiss mathematician Leonard Euler (1707-1783) did however work further on many of Fermats theorems
and "later proved that there are no solutions when the exponent is 3" and "unfortunately, an infinite number of cases remained and the case-by-case method was doomed to fail" (Levine,
1998, p. 1485; Singh, 1997). Leonard Euler was born in Basle, Switzerland in 1707 and began to study theology at the request of his family. His mathematical expertise soon began
to surface and Johann Bernoulli convinced Euler to pursue mathematics full time. As a mathematician, Euler published over 866 books and papers and among his many other contributions, also introduced
the symbols of e, i, f(x), pi, and sigma for summations (Bailey, 1999). Euler spent most of his time solving many of the theorems of Fermat and during this time
he came across Fermats Last Theorem or conjecture in regards to a "proof that Fermat had developed for the case n = 4 that used a method called infinite descent"
...