Gianfrancesco Malfatti

Gianfrancesco Malfatti ( born September 26, 1731 in Ala; † October 9, 1807 in Ferrara) was an Italian mathematician who was able, among other things, resolve all resolvable quintic equations by radicals. After the Malfatti Malfatti circle and the Malfatti problem are named (his solution he found in 1802 and published it in 1803 )

Malfatti studied at a Jesuit school in Verona and then at the College of St. Francis Xavier, University of Bologna, among others, by Vincenzo Riccati, Maria Zanotti, Gabriele Manfredi. 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, when it was reopened.

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

In a work of 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 at proof Nichtauflösbarkeit of equations higher than quartic by radicals, which he criticized (1804 ).

Under Malfatti problem is today understood two different problems: Malfatti gave the Malfatti circles as a solution to today marble problem of Malfatti problem mentioned in: Pack of three circles in a triangle, so that they have maximum area, but do not overlap. It was but since H. praise and HW Richmond 1930 known that these do not always provide the optimal solution, even later it was shown that they even do so only rarely. The optimal solution found Viktor Salgaller and GA Loss 1994. This is distinguished from the design problem of Malfatti, delegating three circles in a triangle so that they touch each other and two sides of the triangle. It has already been solved in the special case of an isosceles triangle by Jakob Bernoulli, also by a Japanese mathematician in the 18th century ( Chokuyen Naonobu Ajima ) and later gave Jakob Steiner (1826, Crelle 's Journal, using basic geometric ) and Alfred Clebsch solutions ( the latter with elliptic functions, 1857 Crelle 's Journal ).

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