Refinable function - Revision history

en>Mark viking: /* top */ Added wl, removed some informal tone

2014-11-22T19:26:21Z

top: Added wl, removed some informal tone

← Older revision		Revision as of 21:26, 22 November 2014
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	~~{{Infobox scientist~~		Hi there. Allow me begin by introducing the writer, her title is Sophia. The favorite hobby for him and his children is fashion and he'll be beginning some thing else alongside [http://kard.dk/?p=24252 real psychic readings] with it. My working day job is an invoicing officer but I've currently utilized for another one. Ohio is exactly where my house is but my spouse desires us to move.<br><br>Here is my website ... [http://si.dgmensa.org/xe/index.php?document_srl=48014&mid=c0102 psychics online] ([http://Chungmuroresidence.com/xe/reservation_branch2/152663 Highly recommended Reading])
	~~\| name = Scipione del Ferro~~
	~~\| image =~~
	~~\| image_size =~~
	~~\| caption =~~
	~~\| birth_date = 6 February 1465~~
	~~\| death_date ={{death date and age\|1526\|11\|5\|1465\|2\|6\|df=yes}}~~
	~~\| residence = [[Bologna]]~~
	~~\| nationality = [[Bologna\|Bolognese]] (Italy)~~
	~~\| field = [[Mathematics]]~~
	~~\| known_for = Solution of the depressed [[cubic equation]]~~
	}}

	~~'''Scipione del Ferro''' (6 February 1465 – 5 November 1526) was an [[Italy\|Italian]] [[mathematics\|mathematician]] who first discovered a method to solve the depressed [[cubic equation]]~~.

	~~==Life==~~
	~~Scipione del Ferro was born in [[Bologna]], in northern [[Italy]], to Floriano and Filippa Ferro. His father, Floriano, worked in~~ the ~~[[paper]] industry~~, which owed its existence to the invention of the [[Printing press\|press]] in the 1450s and which probably allowed Scipione to access various works during early stages of his life. He married and had a daughter, who was named Filippa after his mother.

	~~He likely studied at the [[University of Bologna]], where he was appointed a lecturer in [[Arithmetic]] and [[Geometry]] in 1496. During his last years, he also undertook commercial work.~~

	~~==Diffusion of his work==~~
	There are no surviving scripts from del Ferro. This is in large part due to his resistance to communicating his works. Instead of publishing his ideas, he would only show them to a small, select group of friends and students.

	It is suspected that this is due to the practice of mathematicians at the time of publicly challenging one another. When a mathematician accepted another's challenge, each mathematician needed to solve the other's problems. The ~~loser in a challenge often lost funding or his university position. Del Ferro was fearful of being challenged~~ and ~~likely kept~~ his ~~greatest work secret so that he could use it to defend himself in the event of a challenge.~~

	Despite this secrecy, he had a notebook where he recorded all his important discoveries. After his death in 1526, this notebook was inherited by his son-in-law [[Hannival Nave]], who was married to del Ferro's daughter, Filippa. Nave was also a [[mathematics\|mathematician]] and a former student of del Ferro's, and he ~~replaced del Ferro at the [[University of Bologna]] after his death.~~

	~~In 1543, [[Gerolamo Cardano]] and [[Ludovico Ferrari]] (one of Cardano~~'~~s students) travelled to~~ [~~[Bologna]] to meet Nave and learn about his late father-in-law's notebook, where the solution to the depressed [[cubic equation]] appeared.~~

	~~==The Solution of the Cubic Equation==~~
	Mathematicians from del Ferro's time knew that the general cubic equation could be simplified to one of two cases called the depressed cubic equation, for positive numbers <math>p</math>,<math>q</math>,<math>x</math>:
	:~~<math>x^3 + px = q \,<~~/~~math>~~
	~~:<math>x^3 = px + q \,<~~/~~math>~~
	~~The term in <math>x^2<~~/~~math> can always be removed by letting <math>x~~=x'~~+a</math>~~ for ~~an appropriate constant <math>a</math>~~.

	~~While it~~ is ~~not known today with certainty the method that del Ferro used, it~~ is thought that he used the fact that <math>x=\sqrt{a+\sqrt{b}}+\sqrt{a-\sqrt{b}}</math> solves the equation <math>x^2=(2\sqrt{a^2-b})x^0+2a</math> to conjecture that <math>x=\sqrt[3]{a+\sqrt{b}}+\sqrt[3]{a-\sqrt{b}}</math> solves <math>x^3=(3\sqrt[3]{a^2-b})x+2a</math>. This turns out to ~~be true~~.

	~~Then with the appropriate substitution of parameters, one can derive a solution to the depressed cubic:~~ <~~math~~>~~\sqrt[3]{\frac{q}{2}+\sqrt{\frac{q^2}{4}+\frac{p^3}{27}}}+\sqrt[3]{\frac{q}{2}-\sqrt{\frac{q^2}{4}+\frac{p^3}{27}}}~~<~~/math~~>

	~~There are conjectures about whether del Ferro worked on a solution to the cubic equation as a result of [[Luca Pacioli]]'s short tenure at the University of Bologna from 1501-1502~~. ~~Pacioli had previously declared in ''Summa de arithmetica'' that he believed a solution to the equation to be impossible, fueling wide interest in the mathematical community~~.

	~~It is unknown whether Scipione del Ferro solved both cases or not~~. ~~However, in 1925, manuscripts were discovered by [[Bartolotti]] which contained del Ferro's method and made [[Bartolotti]] suspect that del Ferro had solved both cases.~~

	[[Gerolamo Cardano\|Cardano]], in his book ''Ars Magna'' (published in 1545) states that it was del Ferro who was the first to solve the cubic equation, and that the [[Cubic equation#Cardano's_method\|solution he gives]] is del Ferro's method.

	~~==Other contributions==~~
	~~Del Ferro also made other important contributions to the rationalization of fractions with denominators containing sums of cube roots.~~

	~~He also investigated geometry problems with a compass set at a fixed angle, but little is known about his work in this area.~~

	~~==References==~~
	*{{cite web\|first =John \|last = O'Connor \|first2=Edmund \|last2=Robertson\|title = MacTutor History of Mathematics\|publisher=University of St. Andrews \| year=1999 \| url=http://~~www-history.mcs.st-andrews~~.ac.uk/~~Biographies~~/~~Ferro~~.~~html}}~~
	*{{cite book\| title= Notable Mathematicians, Online Edition \|publisher = Gale Group}}
	*{{cite book\| title= Ars Magna \| year=1545 \| first=Girolana \|last=Cardano}}
	*{{cite book\| title= Dictionary of Scientific Biography \| first=~~Arnaldo \|last= Masotti \|pages =595–597}}~~
	*{{cite book\| first=Orlando \| last=Merino \| title=A short history of complex numbers \| year=2006}}
	*{{cite book\|first= Alejandro \|last=García Venturini\|title=Matemáticos Que Hicieron Historia}}
	*{{cite book\|first=Ian \|last=Stewart\|title=Galois Theory, Third Edition\|publisher=Chapman & ~~Hall/CRC Mathematics\|year~~=~~2004}}~~

	~~{{Persondata <!-- Metadata: see~~ [~~[Wikipedia~~:~~Persondata]]~~. ~~-->~~
	~~\| NAME = Ferro, Scipione Del~~
	~~\| ALTERNATIVE NAMES =~~
	~~\| SHORT DESCRIPTION = Italian mathematician~~
	~~\| DATE OF BIRTH = 6 February 1465~~
	~~\| PLACE OF BIRTH =~~
	~~\| DATE OF DEATH = 5 November 1526~~
	~~\| PLACE OF DEATH =~~
	}}
	~~{{DEFAULTSORT:Ferro, Scipione Del}}~~
	~~[[Category:1465 births]]~~
	~~[[Category:1526 deaths]]~~
	~~[[Category:People from Bologna]]~~
	~~[[Category:15th-century Italian mathematicians]]~~
	~~[[Category:16th-century Italian mathematicians]~~]

en>Stemonitis: Reverted edits by Red Slash (talk) to last version by Addbot

2013-05-03T06:03:55Z

Reverted edits by Red Slash (talk) to last version by Addbot

← Older revision		Revision as of 08:03, 3 May 2013
Line 1:		Line 1:
	~~Andera~~ is ~~what you~~ ~~best~~ [~~http://kpupf~~.~~com/xe/talk/735373 live psychic reading~~] ([~~http://www.010~~-~~5260~~-~~5333~~.~~com~~/~~index.php?document_srl~~=~~1880&mid~~=~~board_ALMP66 http:~~//~~www~~.~~010~~-~~5260~~-~~5333.com~~/]) can ~~contact her but she never truly favored~~ that ~~name~~. ~~North Carolina~~ is ~~exactly where we~~'~~ve been residing for years~~ and ~~will never transfer~~. ~~One of~~ the ~~issues she enjoys most~~ is ~~canoeing and she~~'s ~~been performing it for fairly~~ a ~~while~~. ~~Distributing production is exactly where my main income comes from and it~~'~~s some thing I really enjoy~~.~~<br><br>My homepage - clairvoyance ([~~http://~~Www~~.~~Publicpledge~~.~~com~~/~~blogs~~/~~post~~/~~7034 linked internet page~~])		{{Infobox scientist
			\| name = Scipione del Ferro
			\| image =
			\| image_size =
			\| caption =
			\| birth_date = 6 February 1465
			\| death_date ={{death date and age\|1526\|11\|5\|1465\|2\|6\|df=yes}}
			\| residence = [[Bologna]]
			\| nationality = [[Bologna\|Bolognese]] (Italy)
			\| field = [[Mathematics]]
			\| known_for = Solution of the depressed [[cubic equation]]
			}}

			'''Scipione del Ferro''' (6 February 1465 – 5 November 1526) was an [[Italy\|Italian]] [[mathematics\|mathematician]] who first discovered a method to solve the depressed [[cubic equation]].

			==Life==
			Scipione del Ferro was born in [[Bologna]], in northern [[Italy]], to Floriano and Filippa Ferro. His father, Floriano, worked in the [[paper]] industry, which owed its existence to the invention of the [[Printing press\|press]] in the 1450s and which probably allowed Scipione to access various works during early stages of his life. He married and had a daughter, who was named Filippa after his mother.

			He likely studied at the [[University of Bologna]], where he was appointed a lecturer in [[Arithmetic]] and [[Geometry]] in 1496. During his last years, he also undertook commercial work.

			==Diffusion of his work==
			There are no surviving scripts from del Ferro. This is in large part due to his resistance to communicating his works. Instead of publishing his ideas, he would only show them to a small, select group of friends and students.

			It is suspected that this is due to the practice of mathematicians at the time of publicly challenging one another. When a mathematician accepted another's challenge, each mathematician needed to solve the other's problems. The loser in a challenge often lost funding or his university position. Del Ferro was fearful of being challenged and likely kept his greatest work secret so that he could use it to defend himself in the event of a challenge.

			Despite this secrecy, he had a notebook where he recorded all his important discoveries. After his death in 1526, this notebook was inherited by his son-in-law [[Hannival Nave]], who was married to del Ferro's daughter, Filippa. Nave was also a [[mathematics\|mathematician]] and a former student of del Ferro's, and he replaced del Ferro at the [[University of Bologna]] after his death.

			In 1543, [[Gerolamo Cardano]] and [[Ludovico Ferrari]] (one of Cardano's students) travelled to [[Bologna]] to meet Nave and learn about his late father-in-law's notebook, where the solution to the depressed [[cubic equation]] appeared.

			==The Solution of the Cubic Equation==
			Mathematicians from del Ferro's time knew that the general cubic equation could be simplified to one of two cases called the depressed cubic equation, for positive numbers <math>p</math>,<math>q</math>,<math>x</math>:
			:<math>x^3 + px = q \,</math>
			:<math>x^3 = px + q \,</math>
			The term in <math>x^2</math> can always be removed by letting <math>x=x'+a</math> for an appropriate constant <math>a</math>.

			While it is not known today with certainty the method that del Ferro used, it is thought that he used the fact that <math>x=\sqrt{a+\sqrt{b}}+\sqrt{a-\sqrt{b}}</math> solves the equation <math>x^2=(2\sqrt{a^2-b})x^0+2a</math> to conjecture that <math>x=\sqrt[3]{a+\sqrt{b}}+\sqrt[3]{a-\sqrt{b}}</math> solves <math>x^3=(3\sqrt[3]{a^2-b})x+2a</math>. This turns out to be true.

			Then with the appropriate substitution of parameters, one can derive a solution to the depressed cubic: <math>\sqrt[3]{\frac{q}{2}+\sqrt{\frac{q^2}{4}+\frac{p^3}{27}}}+\sqrt[3]{\frac{q}{2}-\sqrt{\frac{q^2}{4}+\frac{p^3}{27}}}</math>

			There are conjectures about whether del Ferro worked on a solution to the cubic equation as a result of [[Luca Pacioli]]'s short tenure at the University of Bologna from 1501-1502. Pacioli had previously declared in ''Summa de arithmetica'' that he believed a solution to the equation to be impossible, fueling wide interest in the mathematical community.

			It is unknown whether Scipione del Ferro solved both cases or not. However, in 1925, manuscripts were discovered by [[Bartolotti]] which contained del Ferro's method and made [[Bartolotti]] suspect that del Ferro had solved both cases.

			[[Gerolamo Cardano\|Cardano]], in his book ''Ars Magna'' (published in 1545) states that it was del Ferro who was the first to solve the cubic equation, and that the [[Cubic equation#Cardano's_method\|solution he gives]] is del Ferro's method.

			==Other contributions==
			Del Ferro also made other important contributions to the rationalization of fractions with denominators containing sums of cube roots.

			He also investigated geometry problems with a compass set at a fixed angle, but little is known about his work in this area.

			==References==
			*{{cite web\|first =John \|last = O'Connor \|first2=Edmund \|last2=Robertson\|title = MacTutor History of Mathematics\|publisher=University of St. Andrews \| year=1999 \| url=http://www-history.mcs.st-andrews.ac.uk/Biographies/Ferro.html}}
			*{{cite book\| title= Notable Mathematicians, Online Edition \|publisher = Gale Group}}
			*{{cite book\| title= Ars Magna \| year=1545 \| first=Girolana \|last=Cardano}}
			*{{cite book\| title= Dictionary of Scientific Biography \| first=Arnaldo \|last= Masotti \|pages =595–597}}
			*{{cite book\| first=Orlando \| last=Merino \| title=A short history of complex numbers \| year=2006}}
			*{{cite book\|first= Alejandro \|last=García Venturini\|title=Matemáticos Que Hicieron Historia}}
			*{{cite book\|first=Ian \|last=Stewart\|title=Galois Theory, Third Edition\|publisher=Chapman & Hall/CRC Mathematics\|year=2004}}

			{{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
			\| NAME = Ferro, Scipione Del
			\| ALTERNATIVE NAMES =
			\| SHORT DESCRIPTION = Italian mathematician
			\| DATE OF BIRTH = 6 February 1465
			\| PLACE OF BIRTH =
			\| DATE OF DEATH = 5 November 1526
			\| PLACE OF DEATH =
			}}
			{{DEFAULTSORT:Ferro, Scipione Del}}
			[[Category:1465 births]]
			[[Category:1526 deaths]]
			[[Category:People from Bologna]]
			[[Category:15th-century Italian mathematicians]]
			[[Category:16th-century Italian mathematicians]]

en>Glenn: +link

2012-08-31T17:25:47Z

+link

New page

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