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

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

. 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, S ...

Trentino Trentino ( lld, Trentin), officially the Autonomous Province of Trento, is an autonomous province of Italy, in the country's far north. The Trentino and South Tyrol constitute the region of Trentino-Alto Adige/Südtirol, an autonomous region ...

Italy Italy ( it, Italia ), officially the Italian Republic, ) or the Republic of Italy, is a country in Southern Europe. It is located in the middle of the Mediterranean Sea, and its territory largely coincides with the homonymous geographical re ...

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 A college (Latin: ''collegium'') is an educational institution or a constituent part of one. A college may be a degree-awarding tertiary educational institution, a part of a collegiate or federal university, an institution offering ...

Bologna Bologna (, , ; egl, label= Emilian, Bulåggna ; lat, Bononia) is the capital and largest city of the Emilia-Romagna region in Northern Italy. It is the seventh most populous city in Italy with about 400,000 inhabitants and 150 different nat ...

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. He moved to Ferrara in 1754, and became a professor at the

University of Ferrara The University of Ferrara ( it, Università degli Studi di Ferrara) is the main university of the city of Ferrara in the Emilia-Romagna region of northern Italy. In the years prior to the First World War the University of Ferrara, with more than 5 ...

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 , also known as Ajima Manzō Chokuyen, was a Japanese mathematician of the Edo period.Smith, David. (1914). His Dharma name was (祖眞院智算量空居士). Work Ajima is credited with introducing calculus into Japanese mathematics. The si ...

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 center In geometry, a triangle center (or triangle centre) is a point in the plane that is in some sense a center of a triangle akin to the centers of squares and circles, that is, a point that is in the middle of the figure by some measure. For example ...

s 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 equation In algebra, a quintic function is a function of the form :g(x)=ax^5+bx^4+cx^3+dx^2+ex+f,\, where , , , , and are members of a field, typically the rational numbers, the real numbers or the complex numbers, and is nonzero. In other words, a q ...

s, and the property of the

lemniscate of Bernoulli In geometry, the lemniscate of Bernoulli is a plane curve defined from two given points and , known as foci, at distance from each other as the locus of points so that . The curve has a shape similar to the numeral 8 and to the ∞ symbol. I ...

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