Scipione del Ferro (6 February 1465 – 5 November 1526) was an Italian mathematician who first discovered a method to solve the depressed cubic equation.
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 press in the 1450s and which probably allowed Scipione to access various works during the 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 there 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 Annibale della Nave, who was married to del Ferro's daughter, Filippa. Nave was also a 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 Lodovico 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 ,,:
The term in can always be removed by letting for an appropriate constant .
While it is not known today with certainty what method del Ferro used, it is thought that he used the fact that solves the equation to conjecture that solves . This turns out to be true.
Then with the appropriate substitution of parameters, one can derive a solution to the depressed cubic:
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 in 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 Bortolotti which contained del Ferro's method and made Bortolotti suspect that del Ferro had solved both cases.
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 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
O'Connor, John; Robertson, Edmund (1999). "MacTutor History of Mathematics". University of St. Andrews.
Notable Mathematicians, Online Edition. Gale Group.
Cardano, Gerolamo (1545). Ars Magna.
Masotti, Arnaldo. Dictionary of Scientific Biography. pp. 595–597.
Merino, Orlando (2006). A short history of complex numbers.
García Venturini, Alejandro. Matemáticos Que Hicieron Historia.
Stewart, Ian (2004). Galois Theory, Third Edition. Chapman & Hall/CRC Mathematics.
January 07, 2023
scipione, ferro, this, article, needs, additional, citations, verification, please, help, improve, this, article, adding, citations, reliable, sources, unsourced, material, challenged, removed, find, sources, news, newspapers, books, scholar, jstor, november, . This article needs additional citations for verification Please help improve this article by adding citations to reliable sources Unsourced material may be challenged and removed Find sources Scipione del Ferro news newspapers books scholar JSTOR November 2021 Learn how and when to remove this template message Scipione del Ferro 6 February 1465 5 November 1526 was an Italian mathematician who first discovered a method to solve the depressed cubic equation Scipione del FerroBorn6 February 1465BolognaDied5 November 1526 1526 11 05 aged 61 BolognaNationalityItalianAlma materUniversity of BolognaKnown forSolving the depressed cubic equationScientific careerFieldsMathematicsInstitutionsUniversity of Bologna Contents 1 Life 2 Diffusion of his work 3 The solution of the cubic equation 4 Other contributions 5 ReferencesLife EditScipione 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 press in the 1450s and which probably allowed Scipione to access various works during the 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 there in Arithmetic and Geometry in 1496 During his last years he also undertook commercial work Diffusion of his work EditThere 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 Annibale della Nave who was married to del Ferro s daughter Filippa Nave was also a 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 Lodovico 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 EditMathematicians 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 p displaystyle p q displaystyle q x displaystyle x x 3 p x q displaystyle x 3 px q x 3 p x q displaystyle x 3 px q The term in x 2 displaystyle x 2 can always be removed by letting x x a displaystyle x x a for an appropriate constant a displaystyle a While it is not known today with certainty what method del Ferro used it is thought that he used the fact that x a b a b displaystyle x sqrt a sqrt b sqrt a sqrt b solves the equation x 2 2 a 2 b x 0 2 a displaystyle x 2 2 sqrt a 2 b x 0 2a to conjecture that x a b 3 a b 3 displaystyle x sqrt 3 a sqrt b sqrt 3 a sqrt b solves x 3 3 a 2 b 3 x 2 a displaystyle x 3 3 sqrt 3 a 2 b x 2a This turns out to be true Then with the appropriate substitution of parameters one can derive a solution to the depressed cubic q 2 q 2 4 p 3 27 3 q 2 q 2 4 p 3 27 3 displaystyle 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 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 in 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 Bortolotti which contained del Ferro s method and made Bortolotti suspect that del Ferro had solved both cases 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 solution he gives is del Ferro s method Other contributions EditDel 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 EditO Connor John Robertson Edmund 1999 MacTutor History of Mathematics University of St Andrews Notable Mathematicians Online Edition Gale Group Cardano Gerolamo 1545 Ars Magna Masotti Arnaldo Dictionary of Scientific Biography pp 595 597 Merino Orlando 2006 A short history of complex numbers Garcia Venturini Alejandro Matematicos Que Hicieron Historia Stewart Ian 2004 Galois Theory Third Edition Chapman amp Hall CRC Mathematics Retrieved from https en wikipedia org w index php title Scipione del Ferro amp oldid 1128502526, wikipedia, wiki, book, books, library,
