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Topic: Abel Ruffini theorem

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	Kids.Net.Au - Encyclopedia > Abel-Ruffini theorem
		The Abel-Ruffini theorem states that there is no general solution in radicals to polynomial equations of degree five or higher.
		The content of the theorem is that the solution of a higher-degree equation cannot always be expressed by starting with the coefficients and using only the operations of addition, subtraction, multiplication, division and extracting roots (radicals).
		The theorem was first proved by Paolo Ruffini[?] in 1799, but his proof was mostly ignored.
	www.kids.net.au /encyclopedia-wiki/ab/Abel-Ruffini_theorem (404 words)

	Abel-Ruffini theorem
		The Abel-Ruffini theorem states that there is no general solution in radicals to polynomial equations of degree five or higher.
		The content of the theorem is that the solution of a higher-degree equation cannot always be expressed by starting with the coefficients and using only the operations of addition, subtraction, multiplication, division and extracting roots (radicals).
		The theorem was first proved by Paolo Ruffini[?] in 1799, but his proof was mostly ignored.
	www.ebroadcast.com.au /lookup/encyclopedia/ab/Abel-Ruffini_theorem.html (379 words)

	Paolo Ruffini Summary
		Ruffini's professional situation changed drastically in 1796, however, when Napoleon's troops occupied Modena and he was appointed representative from the department of Panaro to the Junior Council of the Cisalpine Republic, against his wishes.
		Ruffini also contributed to the development of group theory, and was known for his work as a philosopher and physician.
		Ruffini himself was such a talented student that he took over instruction of Cassiani's foundations of analysis course when the latter had to take a leave of absence in 1787.
	www.bookrags.com /Paolo_Ruffini (1352 words)

	AllRefer.com - Ruffini, Paolo Information
		He published a theorem stating that it was impossible to give a general solution to equations of greater than the fourth degree using only radicals (such as square roots, cube roots, and so on).
		Ruffini was born in Valentano, Viterbo, and studied at Modena.
		Ruffini made a substantial contribution to the theory of equations, developing the so-called theory of substitutions, which was the forerunner of modern group theory.
	www.allrefer.com /ruffini-paolo (244 words)

	Read This: Abel's Proof
		But from 1799 to 1813 the physician and mathematician Ruffini presented six versions of a proof of the quintic's unsolvability, a proof that was difficult for most mathematiicans of the time to understand (although Cauchy expressed his admiration) and was ultimately seen to be incomplete.
		Abel's "...insight [connecting] solvability with commutativity" is followed (after biographical details of Galois' tragic life) by Galois' reformulation of the mathematical situation in what we now recognize as group theory.
		Appendix B is Abel's elaboration on the form that a quintic solution must take, and Appendix C describes a theorem of Cauchy on permutations that is crucial in the overall proof.
	www.maa.org /reviews/abelsproof.html (972 words)

	Galois Theory for Beginners
		This question was resolved in 1826 by Niels Henrik Abel (1802— 1829), who showed that there cannot exist general solution formulas for equations of the fifth and higher degree that involve only the usual arithmetic operations and extraction of roots.
		The heart of Abel’s proof is that for the intermediate values that would appear in a hypothetically existing formula, one could prove corresponding symmetries among the various solutions of the equation that would lead to a contradiction.
		A generalization of Abel’s approach, which was applicable to all polynomial equations, was found a few years later by the twenty-year-old Evariste Galois (1811—1832).
	www.galois-theorie.de /galois-theory.htm (1004 words)

	RUFFINI, Paolo, Teoria Generale delle Equazioni, in cui si dimostra impossibile la soluzione algebraica dell equazioni ...
		RUFFINI, Paolo, Teoria Generale delle Equazioni, in cui si dimostra impossibile la soluzione algebraica dell equazioni generali di grado superiore al quarto...
		First edition of the first announcement of the Abel-Ruffini theorem, 'a general algebraic equation of higher than the fourth degree cannot be solved by means of radical-rational operations...
		Following its independent demonstration by Abel in 1824, the theorem eventually took its place in the general theory of the solubility of algebraic equations that Galois constructed on the basis of the theory of permutation groups' (DSB, q.v.
	www.polybiblio.com /watbooks/2253.html (303 words)

	Abel–Ruffini theorem: Encyclopedia - Abel–Ruffini theorem
		The Abel–Ruffini theorem states that there is no general solution in radicals to polynomial equations of degree five or higher.
		In fact, if the polynomial has real or complex coefficients, and we allow complex solutions, then every polynomial equation has solutions; this is the fundamental theorem of algebra.
		The content of the theorem is that the solution of a higher-degree equation cannot always be expressed by starting with the coefficients and using only finitely many of the operations of addition, subtraction, multiplication, division and extracting roots (radicals).
	www.experiencefestival.com /a/AbelRuffini_theorem/id/409793 (579 words)

	Math Forum Discussions - Re: Abel-Ruffini Theorem
		> all the results needed to prove Abel-Ruffini theorem.
		> necessary lemmas to the proof of the theorem.
		> Note: The Abel-Ruffini theorem says that there are some equations of
	www.mathforum.org /kb/thread.jspa?forumID=13&threadID=60468&messageID=242439 (198 words)

	Abel–Ruffini theorem - History
		Abel–Ruffini theorem - History is one of the topics in focus at Global Oneness.
		Abel–Ruffini theorem - History: Encyclopedia - Abel–Ruffini theorem
		Please rate this archive with 10 as very good and 1 as very poor.
	www.experiencefestival.com /abelruffini_theorem_-_history (265 words)

	Abel's theorem \| English \| Dictionary & Translation by Babylon (Site not responding. Last check: )
		For Abel's theorem on algebraic curves, see Jacobian variety.
		For Abel's theorem on the insolubility of the quintic equation with radicals, see Abel-Ruffini theorem.In real analysis, Abel's theorem for power series relates a limit of a power series to the sum of its coefficients.
		It is named after Norwegian mathematician Niels Henrik Abel.
	www.babylon.com /definition/Abel's_theorem (71 words)

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