Gian Francesco Malfatti
Encyclopedia
Giovanni Francesco Giuseppe, also known as Gian Francesco or Gianfrancesco (26 September 1731-9 October 1807) was an Italian
mathematician
. He was born in Ala, Trentino, Italy
and died in Ferrara
.
Malfatti studied at the College of San Francesco Saverio in Bologna
where his mentors included Vincenzo Riccati
, F. M. Zanotti and G. Manfredi. 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.
Malfatti posed the problem of carving three circular column
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
after his work, despite the earlier work of Japanese mathematician Ajima Naonobu and of his countryman Gilio di Cecco da Montepulciano on the same problem and despite the fact that the conjecture was later proven false. Several triangle center
s derived from these circles are also named after both Ajima and Malfatti.
Additional topics in Malfatti's research concerned quintic equation
s, 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.
Italy
Italy , officially the Italian Republic languages]] under the European Charter for Regional or Minority Languages. In each of these, Italy's official name is as follows:;;;;;;;;), is a unitary parliamentary republic in South-Central Europe. To the north it borders France, Switzerland, Austria and...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
. He was born in Ala, Trentino, Italy
Italy
Italy , officially the Italian Republic languages]] under the European Charter for Regional or Minority Languages. In each of these, Italy's official name is as follows:;;;;;;;;), is a unitary parliamentary republic in South-Central Europe. To the north it borders France, Switzerland, Austria and...
and died in Ferrara
Ferrara
Ferrara is a city and comune in Emilia-Romagna, northern Italy, capital city of the Province of Ferrara. It is situated 50 km north-northeast of Bologna, on the Po di Volano, a branch channel of the main stream of the Po River, located 5 km north...
.
Malfatti studied at the College of San Francesco Saverio in Bologna
Bologna
Bologna is the capital city of Emilia-Romagna, in the Po Valley of Northern Italy. The city lies between the Po River and the Apennine Mountains, more specifically, between the Reno River and the Savena River. Bologna is a lively and cosmopolitan Italian college city, with spectacular history,...
where his mentors included Vincenzo Riccati
Vincenzo Riccati
Vincenzo Riccati was an Italian mathematician and physicist. He was the brother of Giordano Riccati, and the second son of Jacopo Riccati....
, F. M. Zanotti and G. Manfredi. He moved to Ferrara in 1754, and became a professor at the University of Ferrara
University of Ferrara
The University of 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 500 students, was the best attended of the free universities in Italy...
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.
Malfatti posed the problem of carving three circular column
Column
A column or pillar in architecture and structural engineering is a vertical structural element that transmits, through compression, the weight of the structure above to other structural elements below. For the purpose of wind or earthquake engineering, columns may be designed to resist lateral forces...
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
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...
after his work, despite the earlier work of Japanese mathematician Ajima Naonobu and of his countryman Gilio di Cecco da Montepulciano on the same problem and despite the fact that the conjecture was later proven false. Several triangle center
Triangle center
In geometry a triangle center is a point in the plane that is in some sense a center of a triangle akin to the centers of squares and circles. For example the centroid, circumcenter, incenter and orthocenter were familiar to the ancient Greeks, and can be obtained by simple constructions. Each of...
s derived from these circles are also named after both Ajima and Malfatti.
Additional topics in Malfatti's research concerned quintic equation
Quintic equation
In mathematics, a quintic function is a function of the formg=ax^5+bx^4+cx^3+dx^2+ex+f,\,where a, b, c, d, e and f are members of a field, typically the rational numbers, the real numbers or the complex numbers, and a is nonzero...
s, and the property of the lemniscate of Bernoulli
Lemniscate of Bernoulli
In geometry, the lemniscate of Bernoulli is a plane curve defined from two given points F1 and F2, known as foci, at distance 2a from each other as the locus of points P so that PF1·PF2 = a2. The curve has a shape similar to the numeral 8 and to the ∞ symbol. Its name is from lemniscus, which is...
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.
External links
- Clark Kimberling's page on Malfatti