Luigi Cremona
Encyclopedia
Luigi Cremona was an Italian
mathematician. His life was devoted to the study of geometry
and reforming advanced mathematical teaching in Italy. His reputation mainly rests on his Introduzione ad una teoria geometrica delle curve piane. He notably enriched our knowledge of algebraic curve
s and algebraic surface
s.
(Lombardy
), then part of the Austria
n controlled Kingdom of Lombardy-Venetia.
In 1848, when Milan
and Venice
rose against Austria, Cremona, then only seventeen, joined the ranks of the Italian volunteers. He remained with them, fighting on behalf of his country's freedom, until, in 1849, the capitulation of Venice
put an end to the campaign.
He then returned to Pavia, where he pursued his studies at the university under Francesco Brioschi
, and determined to seek a career as teacher of mathematics. His first appointment was as elementary mathematical master at the gymnasium and lyceum of Cremona
, and he afterwards obtained a similar post at Milan
. In 1860 he was appointed to the professorship of higher geometry at the University of Bologna
, and in 1866 to that of higher geometry and graphical statics at the higher technical college of Milan. In this same year he competed for the Steiner Prize of the Berlin Academy, with a treatise entitled Memoria sulle superfici del terzo ordine, and shared the award with J. C. F. Sturm. Two years later the same prize was conferred on him without competition.
In 1873 he was called to Rome to organize the college of engineering, and was also appointed professor of higher mathematics at the university. Cremona's reputation had now become European, and in 1879 he was elected a corresponding member of the Royal Society
. In the same year he was made a senator of the Kingdom of Italy
.
As early as 1856 Cremona had begun to contribute to the Annali di scienze matematiche e fisiche, and to the Annali di matematica, of which he became afterwards joint editor. Papers by him appeared in the mathematical journals of Italy, France, Germany and England, and he published several important works, many of which have been translated into other languages. His manual on Graphical Statics
and his Elements of Projective Geometry (translated by C. Leudesdorf), have been published in English by the Clarendon Press.
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. His life was devoted to the study of geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
and reforming advanced mathematical teaching in Italy. His reputation mainly rests on his Introduzione ad una teoria geometrica delle curve piane. He notably enriched our knowledge of algebraic curve
Algebraic curve
In algebraic geometry, an algebraic curve is an algebraic variety of dimension one. The theory of these curves in general was quite fully developed in the nineteenth century, after many particular examples had been considered, starting with circles and other conic sections.- Plane algebraic curves...
s and algebraic surface
Algebraic surface
In mathematics, an algebraic surface is an algebraic variety of dimension two. In the case of geometry over the field of complex numbers, an algebraic surface has complex dimension two and so of dimension four as a smooth manifold.The theory of algebraic surfaces is much more complicated than that...
s.
Biography
Luigi Cremona was born in PaviaPavia
Pavia , the ancient Ticinum, is a town and comune of south-western Lombardy, northern Italy, 35 km south of Milan on the lower Ticino river near its confluence with the Po. It is the capital of the province of Pavia. It has a population of c. 71,000...
(Lombardy
Lombardy
Lombardy is one of the 20 regions of Italy. The capital is Milan. One-sixth of Italy's population lives in Lombardy and about one fifth of Italy's GDP is produced in this region, making it the most populous and richest region in the country and one of the richest in the whole of Europe...
), then part of the Austria
Austria
Austria , officially the Republic of Austria , is a landlocked country of roughly 8.4 million people in Central Europe. It is bordered by the Czech Republic and Germany to the north, Slovakia and Hungary to the east, Slovenia and Italy to the south, and Switzerland and Liechtenstein to the...
n controlled Kingdom of Lombardy-Venetia.
In 1848, when Milan
Milan
Milan is the second-largest city in Italy and the capital city of the region of Lombardy and of the province of Milan. The city proper has a population of about 1.3 million, while its urban area, roughly coinciding with its administrative province and the bordering Province of Monza and Brianza ,...
and Venice
Venice
Venice is a city in northern Italy which is renowned for the beauty of its setting, its architecture and its artworks. It is the capital of the Veneto region...
rose against Austria, Cremona, then only seventeen, joined the ranks of the Italian volunteers. He remained with them, fighting on behalf of his country's freedom, until, in 1849, the capitulation of Venice
Venice
Venice is a city in northern Italy which is renowned for the beauty of its setting, its architecture and its artworks. It is the capital of the Veneto region...
put an end to the campaign.
He then returned to Pavia, where he pursued his studies at the university under Francesco Brioschi
Francesco Brioschi
Francesco Brioschi was an Italian mathematician.Brioschi was born in Milan in 1824. From 1850 he taught analytical mechanics in the University of Pavia. After the Italian unification in 1861, he was elected depute in the Parliament of Italy and then appointed twice secretary of the Education...
, and determined to seek a career as teacher of mathematics. His first appointment was as elementary mathematical master at the gymnasium and lyceum of Cremona
Cremona
Cremona is a city and comune in northern Italy, situated in Lombardy, on the left bank of the Po River in the middle of the Pianura Padana . It is the capital of the province of Cremona and the seat of the local City and Province governments...
, and he afterwards obtained a similar post at Milan
Milan
Milan is the second-largest city in Italy and the capital city of the region of Lombardy and of the province of Milan. The city proper has a population of about 1.3 million, while its urban area, roughly coinciding with its administrative province and the bordering Province of Monza and Brianza ,...
. In 1860 he was appointed to the professorship of higher geometry at the University of Bologna
University of Bologna
The Alma Mater Studiorum - University of Bologna is the oldest continually operating university in the world, the word 'universitas' being first used by this institution at its foundation. The true date of its founding is uncertain, but believed by most accounts to have been 1088...
, and in 1866 to that of higher geometry and graphical statics at the higher technical college of Milan. In this same year he competed for the Steiner Prize of the Berlin Academy, with a treatise entitled Memoria sulle superfici del terzo ordine, and shared the award with J. C. F. Sturm. Two years later the same prize was conferred on him without competition.
In 1873 he was called to Rome to organize the college of engineering, and was also appointed professor of higher mathematics at the university. Cremona's reputation had now become European, and in 1879 he was elected a corresponding member of the Royal Society
Royal Society
The Royal Society of London for Improving Natural Knowledge, known simply as the Royal Society, is a learned society for science, and is possibly the oldest such society in existence. Founded in November 1660, it was granted a Royal Charter by King Charles II as the "Royal Society of London"...
. In the same year he was made a senator of the Kingdom of 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...
.
As early as 1856 Cremona had begun to contribute to the Annali di scienze matematiche e fisiche, and to the Annali di matematica, of which he became afterwards joint editor. Papers by him appeared in the mathematical journals of Italy, France, Germany and England, and he published several important works, many of which have been translated into other languages. His manual on Graphical Statics
Statics
Statics is the branch of mechanics concerned with the analysis of loads on physical systems in static equilibrium, that is, in a state where the relative positions of subsystems do not vary over time, or where components and structures are at a constant velocity...
and his Elements of Projective Geometry (translated by C. Leudesdorf), have been published in English by the Clarendon Press.
Works
- Introduzione ad una teoria geometrica delle curve piane (Tipi Gamberini e Parmeggiani, Bologna, 1862)
- Opere matematiche di Luigi Cremona; pubblicati sotto gli auspici della R. Accademia dei Lincei (U. Hoepli, Milano, 1914)
- Elements of projective geometry (Clarendon press, Oxford, 1885) (translation by Charles Leudesdorf)
- Graphical statics. Two treatises on the graphical calculus and reciprocal figures in graphical statics (Clarendon press, Oxford, 1890) (Translated by Thomas Hudson Beare.)
See also
- Cremona diagramCremona diagramThe Cremona diagram is a graphical method used in statics of trusses to determine the forces in members . The method was created by the Italian mathematician Luigi Cremona....
- Cremona groupCremona groupIn mathematics, in birational geometry, the Cremona group of order n over a field k is the group of birational automorphisms of the n-dimensional projective space over k...
- Cremona–Richmond configuration
- TrussTrussIn architecture and structural engineering, a truss is a structure comprising one or more triangular units constructed with straight members whose ends are connected at joints referred to as nodes. External forces and reactions to those forces are considered to act only at the nodes and result in...