Malfatti, Gian Francesco
MALFATTI, GIAN FRANCESCO
(b Ala, Trento, Italy, 1731; d. Ferrara, Italy, 9 October 1807)
After completing his studies in Bologna under the guidance of Francesco Maria Zanotti, Gabriele Manfredi, and Vincenzo Riccati, Malfatti went to Ferrara in 1754, where he founded a school of mathematics and physics. In 1771, when the University of Ferrara was reestablished, he was appointed professor of mathematics. He held this post for about thirty years, teaching all phases of mathematics from Euclidean geometry to calculus.
Malfatti became famous for his paper “De aequationibus quadrato-cubicis disquisitio analytica” (1770), in which, given an equation of the fifth degree, he constructed a resolvent of the equation of the sixth degree, that is, the well-known Malfatti resolvent. If the root is known, the complete resolution of the given equation may be deduced. The latter, however, cannot be obtained by means of rational root expressions; rather, as Brioschi later demonstrated, it is obtained by means of elliptical transcendents.
Malfatti also demonstrated that a memoir on the theory of probability, published by Lagrange in 1774 and proclaimed by Poisson as “one of Lagrange’s most beautiful works,” nevertheless required explanation at one point.
In a brief treatise entitled Della curva cassiniana (1781), Malfatti demonstrated that a special case of Cassini’s curve, the lemniscate, has the property that a mass point moving on it under gravity goes along any are of the curve in the same time as it traverses the subtending chord.
In 1802 Malfatti gave the first, brilliant solution of the problem that bears his name: “Describe in a triangle three circumferences that are mutually tangent, each of which touches two sides of the triangle.” Many illustrious mathematicians had dealt with this problem. Jacques Bernoulli (1654–1705) had earlier dealt with the special case in which the triangle is isosceles. An elegant geometric solution was supplied by Steiner (Crelle’s Journal, vol. 1, 1826), while Clebsch, dealing with the same problem in 1857, made an excellent application of the elliptical functions (Crelle’s Journal, vol. 53, 1857).
In a letter to A. M. Lorgna (27 April 1783), Malfatti gave the polar equation concerning the squaring of the circle.
I. Original Works. Among Malfatti’s works are “De aequationibus quadrato-cubicis disquisitio analytica,” in Atti dell’ Accademia dei Fisiocritici di Siena(1770);Memorie della Societá italiana delle scienze detta dei XL, 3 ; Della curva cassiniana (Pavia, 1781); Memorie della Societá italiana delle scienze detta dei XL, 10 (1802); and his letter to Lorgna, inBullettino di bibliografia e di storia delle scienze matematiche e fisiche, 9 (1876), 438.
II. Secondary Literature. For further information on Malfatti and his work, see G. B. Biadego, “Intorno alla vita e agli scritti di Gianfrancesco Malfatti, matematico del sec. XVIII°,” in Bullettino di bibliografia e storia delle matematiche del Boncompagni, 9 (1876); E. Bortolotti, “Sulla risolvente di Malfatti,” in Atti dell’ Accademia di Modens, 3rd ser., 7 (1906); “Commemorazione di G. F. Malfatti,” in Atti della XIX riunione della Societá italiana per il progresso delle scienze (1930). Also see article on Malfatti in Enciclopedia italiana (Milan, 1934), XXII, 16; F. Brioschi, “Sulla risolvente di Malfatti,” in Memorie dell’ Istituto lombardo di scienze e lettere, 9 (1863); Gino Loria, Curve piane speciali: Teoria e storia (Milan, 1930), I, 265, and II, 23; and Storia delle matematiche, 2nd ed. (Milan, 1950), passim; A. Procissi, “Questioni connesse al problema di Malfatti e bibliografia,” in Periodico di matematiche, 4th ser., 12 (1932); and A. Wittstein, Geschichte des Malfatti’ schen Problems (Munich, 1871).
"Malfatti, Gian Francesco." Complete Dictionary of Scientific Biography. . Encyclopedia.com. (November 18, 2018). https://www.encyclopedia.com/science/dictionaries-thesauruses-pictures-and-press-releases/malfatti-gian-francesco
"Malfatti, Gian Francesco." Complete Dictionary of Scientific Biography. . Retrieved November 18, 2018 from Encyclopedia.com: https://www.encyclopedia.com/science/dictionaries-thesauruses-pictures-and-press-releases/malfatti-gian-francesco
Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).
Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.
Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the most-recent information available at these sites:
Modern Language Association
The Chicago Manual of Style
American Psychological Association
- Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most Encyclopedia.com content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
- In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.