Giovanni Francesco Giuseppe Malfatti, also known as Gian Francesco or Gianfrancesco (26 September 1731 – 9 October 1807) was an Italian mathematician. He was born in

Ala Ala, ALA, Alaa or Alae may refer to: Places * Ala, Hiiu County, Estonia, a village * Ala, Valga County, Estonia, a village * Ala, Alappuzha, Kerala, India, a village * Ala, Iran, a village in Semnan Province * Ala, Gotland, Sweden * Alad, Seydu ...

, Trentino, Italy and died in

Ferrara Ferrara (, ; egl, Fràra ) is a city and ''comune'' in Emilia-Romagna, northern Italy, capital of the Province of Ferrara. it had 132,009 inhabitants. It is situated northeast of Bologna, on the Po di Volano, a branch channel of the main stream ...

. Malfatti studied at the College of San Francesco Saverio in Bologna where his mentors included

Vincenzo Riccati Vincenzo Riccati (Castelfranco Veneto, 11 January 1707 – Treviso, 17 January 1775) was a Venetian mathematician and physicist. Life Vincenzo Riccati was the brother of Giordano Riccati, and the second son of Jacopo Riccati. He entered the ...

, F. M. Zanotti and

Gabriele Manfredi Gabriele Manfredi (25 March 1681 – 13 October 1761) was an Italian mathematician who undertook important work in the field of calculus. Early years Gabriele Manfredi was born in Bologna, then in the Papal States, on 25 March 1681. He was the s ...

. He moved to Ferrara in 1754, and became a professor at the University of Ferrara when it was re-established in 1771. In 1782 he was one of the founders of the ''Societa Italiana delle Scienze'', later to become the

Accademia nazionale delle scienze detta dei XL The Accademia Nazionale delle Scienze (), or more formally L'Accademia Nazionale delle Scienze detta dei XL, and also called the Accademia dei XL (), is Italy's national academy of science. Its offices are located within the Villino Rosso, at the co ...

Contributions to mathematics

In 1803, Malfatti posed the problem of carving three circular

column A column or pillar in architecture and structural engineering is a structural element that transmits, through compression, the weight of the structure above to other structural elements below. In other words, a column is a compression member. ...

s out of a triangular block of marble, using as much of the marble as possible, and conjectured that three mutually-tangent circles inscribed within the triangle would provide the optimal solution. These tangent circles are now known as

Malfatti circles In geometry, the Malfatti circles are three circles inside a given triangle such that each circle is tangent to the other two and to two sides of the triangle. They are named after Gian Francesco Malfatti, who made early studies of the problem o ...

after his work, despite the earlier work of Japanese mathematician Ajima Naonobu and of Malfatti's countryman Gilio di Cecco da Montepulciano on the same problem and despite the fact that the conjecture was later proven false. Several triangle centers derived from these circles are also named after both Ajima and Malfatti.C. Kimberling
Encyclopedia of Triangle Centers
, X(179), X(180), and X(400). Lemniscate gravity

Malfatti - De natura radicum in aequationibus quarti gradus, 1758 - 1402537

Additional topics in Malfatti's research concerned quintic equations, and the property of the lemniscate of Bernoulli that a ball rolling down an arc of the lemniscate, under the influence of gravity, will take the same time to traverse it as a ball rolling down a straight line segment connecting the endpoints of the arc.

Selected publications

Notes

References

* * Leonardo Franchini, "La matematica e il gioco del lotto - Una biografia di Gianfrancesco Malfatti", Edizioni Stella, Rovereto, ottobre 2007.

External links

* Clark Kimberling's page o
Malfatti
* Leonardo Franchini, "La matematica e il gioco del lotto - Una biografia di Gianfrancesco Malfatti", Edizioni Stella, Rovereto, ottobre 2007. {{DEFAULTSORT:Malfatti, Gian Francesco 1731 births 1807 deaths People from Ala, Trentino 18th-century Italian mathematicians 19th-century Italian mathematicians