Gianfrancesco Malfatti

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Gianfrancesco Malfatti

Gianfrancesco Malfatti (born September 26, 1731 in Ala , † October 9, 1807 in Ferrara ) was an Italian mathematician who managed, among other things, to solve all fifth-degree equations that could be solved by radicals . The Malfatti circle and the Malfatti problem are named after Malfatti (he found his solution in 1802 and published it in 1803)

Malfatti studied at a Jesuit school in Verona and then at the College of San Francesco Saverio at the University of Bologna with Vincenzo Riccati , Maria Zanotti , Gabriele Manfredi, among others . From 1754 he taught mathematics and physics at a school in Ferrara, which he founded there. In 1771 he became professor of mathematics at the University of Ferrara there when it was reopened.

In 1782 he was one of the founders of the Societa Italiana delle Scienze.

De natura radicum in aequationibus quarti gradus , 1758

In a work from 1770 ( De aequationibus quadrato-cubicis disquisitio analytica ) constructed a solution of special equations of the fifth degree with the later so-called Malfatti resolvent . This work made him known. He was involved in the discussion of Paolo Ruffini's early attempts to prove the insolvability of equations of higher than fourth degree by radicals, which he criticized (1804).

Today, the Malfatti problem is understood to mean two different problems: Malfatti gave the Malfatti circles as a solution to the problem that Malfatti now calls the marble problem : Packing three circles into a triangle so that they have a maximum area but do not overlap. However, it was known from H. Lob and HW Richmond in 1930 that these do not always deliver the optimal solution, and later it was shown that they rarely do this. Wiktor Salgaller and GA Loss found the optimal solution in 1994. This is differentiated from Malfatti's construction problem of inscribing three circles in a triangle so that they touch each other and two sides of the triangle. It was already solved in the special case of the isosceles triangle by Jakob I Bernoulli , and about 30 years before Malfatti by the Japanese Ajima Naonobu and later Jakob Steiner (1826, Crelle's Journal, in a purely geometric way) and Alfred Clebsch gave solutions (the latter with elliptical functions, 1857, Crelle's Journal).

In addition to geometry and the question of solving algebraic equations of a higher degree, he also dealt with finite difference methods , mechanics (for example movement of a mass point in the gravitational field on a lemniscate in 1781), analysis and probability theory (here, for example, he found an error in a Work by Joseph-Louis Lagrange from 1774).

literature

  • Constantin von Wurzbach : Malfatti, Johann Franz . In: Biographisches Lexikon des Kaiserthums Oesterreich . 16th part. Imperial and Royal Court and State Printing Office, Vienna 1867, p. 330 ( digital copy ).
  • L. Pepe, L. Biasini, L. Capra, M. Fiorentini (editors) Gianfrancesco Malfatti nella cultura del suo tempo , Atti di Convegno 23–24 ottobre 1981, Università degli Studi di Ferrara, Ferrara, 1982 (including an essay by Enrico Giusti on work on Malfatti's analysis)
  • Leonardo Franchini La matematica e il gioco del lotto - Una biografia di Gianfrancesco Malfatti , Edizioni Stella, Rovereto, 2007.
  • Marco Andreatta, Andras Bezdek, Jan P. Boronski The Malfatti Problem: two centuries of debate , Mathematical Intelligencer, 2011, No. 1

Web links

swell

  1. ↑ Malfatti Memoria sopra un problema stereotomico , Memorie di matematica e fisica della Societé Italiana delle Scienze, Volume 10, 1803, pp. 235–244
  2. ↑ Praise, Richmond On the Solution of Malfatti's Problem for a Triangle , Proc. London Math. Soc. 2, 287-304, 1930
  3. ^ Zalgaller, GA Los: The solution of Malfatti's problem . Journal of Mathematical Sciences, Vol. 72, No. 4, 1994, pp. 3163-3177
personal data
SURNAME Malfatti, Gianfrancesco
BRIEF DESCRIPTION Italian mathematician
DATE OF BIRTH September 26, 1731
PLACE OF BIRTH Ala , then Kronland Tirol now Italy
DATE OF DEATH October 9, 1807
Place of death Ferrara , Italy