Eugène Charles Catalan
Encyclopedia
Eugène Charles Catalan was a French
and Belgian
mathematician
.
(now Belgium
, then part of the First French Empire
), the only child of a French jeweller by the name of Joseph Catalan, in 1814. In 1825, he traveled to Paris and learned mathematics at École Polytechnique
, where he met Joseph Liouville
(1833). In 1834 he was expelled from university and went to Châlons-sur-Marne
, where he received a post after graduating. Catalan came back to the École Polytechnique, and, with the help of Liouville, obtained his degree in mathematics in 1841. He went on to Charlemagne College to teach descriptive geometry. Though he was politically active and strongly left-wing, leading him to participate in the 1848 Revolution, he had an animated career and also sat in the France's Chamber of Deputies. Later, in 1849, Catalan was visited at his home by the French Police, searching for illicit teaching material; however, none was found.
The University of Liège
appointed him chair of analysis in 1865. In 1879, still in Belgium, he became journal editor where he published as a foot note Paul-Jean Busschop's theory after refusing it in 1873 - letting Busschop know that it was too empirical. In 1883, he worked for the Belgian Academy of Science
in the field of number theory. He died in Liège, Belgium
where he had received a chair.
s, descriptive geometry
, number theory
and combinatorics
. He gave his name to a unique surface (periodic minimal surface in the space
) that he discovered in 1855. Before that, he had stated the famous Catalan's conjecture, which was published in 1844 and was eventually proved in 2002, by the Romania
n mathematician Preda Mihăilescu
. He introduced the Catalan number
s to solve a combinatorial
problem
.
France
The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...
and Belgian
Belgium
Belgium , officially the Kingdom of Belgium, is a federal state in Western Europe. It is a founding member of the European Union and hosts the EU's headquarters, and those of several other major international organisations such as NATO.Belgium is also a member of, or affiliated to, many...
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....
.
Biography
Catalan was born in BrugesBruges
Bruges is the capital and largest city of the province of West Flanders in the Flemish Region of Belgium. It is located in the northwest of the country....
(now Belgium
Belgium
Belgium , officially the Kingdom of Belgium, is a federal state in Western Europe. It is a founding member of the European Union and hosts the EU's headquarters, and those of several other major international organisations such as NATO.Belgium is also a member of, or affiliated to, many...
, then part of the First French Empire
First French Empire
The First French Empire , also known as the Greater French Empire or Napoleonic Empire, was the empire of Napoleon I of France...
), the only child of a French jeweller by the name of Joseph Catalan, in 1814. In 1825, he traveled to Paris and learned mathematics at École Polytechnique
École Polytechnique
The École Polytechnique is a state-run institution of higher education and research in Palaiseau, Essonne, France, near Paris. Polytechnique is renowned for its four year undergraduate/graduate Master's program...
, where he met Joseph Liouville
Joseph Liouville
- Life and work :Liouville graduated from the École Polytechnique in 1827. After some years as an assistant at various institutions including the Ecole Centrale Paris, he was appointed as professor at the École Polytechnique in 1838...
(1833). In 1834 he was expelled from university and went to Châlons-sur-Marne
Châlons-en-Champagne
Châlons-en-Champagne is a city in France. It is the capital of both the department of Marne and the region of Champagne-Ardenne, despite being only a quarter the size of the city of Reims....
, where he received a post after graduating. Catalan came back to the École Polytechnique, and, with the help of Liouville, obtained his degree in mathematics in 1841. He went on to Charlemagne College to teach descriptive geometry. Though he was politically active and strongly left-wing, leading him to participate in the 1848 Revolution, he had an animated career and also sat in the France's Chamber of Deputies. Later, in 1849, Catalan was visited at his home by the French Police, searching for illicit teaching material; however, none was found.
The University of Liège
University of Liège
The University of Liège , in Liège, Wallonia, Belgium, is a major public university in the French Community of Belgium. Its official language is French.-History:...
appointed him chair of analysis in 1865. In 1879, still in Belgium, he became journal editor where he published as a foot note Paul-Jean Busschop's theory after refusing it in 1873 - letting Busschop know that it was too empirical. In 1883, he worked for the Belgian Academy of Science
The Royal Academies for Science and the Arts of Belgium
There are two Royal Academies for Science and the Arts in Belgium, corresponding to the two main languages of the country, Dutch and French . The Academies are located in the Palace of Academies in Brussels....
in the field of number theory. He died in Liège, Belgium
Belgium
Belgium , officially the Kingdom of Belgium, is a federal state in Western Europe. It is a founding member of the European Union and hosts the EU's headquarters, and those of several other major international organisations such as NATO.Belgium is also a member of, or affiliated to, many...
where he had received a chair.
Work
He worked on continued fractionContinued fraction
In mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this other number as the sum of its integer part and another reciprocal, and so on...
s, descriptive geometry
Descriptive geometry
Descriptive geometry is the branch of geometry which allows the representation of three-dimensional objects in two dimensions, by using a specific set of procedures. The resulting techniques are important for engineering, architecture, design and in art...
, number theory
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
and combinatorics
Combinatorics
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size , deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria ,...
. He gave his name to a unique surface (periodic minimal surface in the space
) that he discovered in 1855. Before that, he had stated the famous Catalan's conjecture, which was published in 1844 and was eventually proved in 2002, by the RomaniaRomania
Romania is a country located at the crossroads of Central and Southeastern Europe, on the Lower Danube, within and outside the Carpathian arch, bordering on the Black Sea...
n mathematician Preda Mihăilescu
Preda Mihailescu
Preda V. Mihăilescu is a Romanian mathematician, best known for his proof of Catalan's conjecture.Born in Bucharest, he is the brother of Vintilă Mihăilescu. After leaving Romania in 1973, he settled in Switzerland. He studied mathematics and computer science in Zürich, receiving his Ph.D. from...
. He introduced the Catalan number
Catalan number
In combinatorial mathematics, the Catalan numbers form a sequence of natural numbers that occur in various counting problems, often involvingrecursively defined objects...
s to solve a combinatorial
Combinatorics
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size , deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria ,...
problem
Catalan's problem
In mathematics, Catalan's problem asks the number of ways n + 1 factors can be completely parenthesized by n pairs of parentheses...
.
See also
- Catalan solidCatalan solidIn mathematics, a Catalan solid, or Archimedean dual, is a dual polyhedron to an Archimedean solid. The Catalan solids are named for the Belgian mathematician, Eugène Catalan, who first described them in 1865....
- Cassini and Catalan identities for Fibonacci numberFibonacci numberIn mathematics, the Fibonacci numbers are the numbers in the following integer sequence:0,\;1,\;1,\;2,\;3,\;5,\;8,\;13,\;21,\;34,\;55,\;89,\;144,\; \ldots\; ....
s - Catalan's constant
- Catalan numberCatalan numberIn combinatorial mathematics, the Catalan numbers form a sequence of natural numbers that occur in various counting problems, often involvingrecursively defined objects...
- Catalan's problemCatalan's problemIn mathematics, Catalan's problem asks the number of ways n + 1 factors can be completely parenthesized by n pairs of parentheses...
- Catalan–Mersenne number/Catalan's Mersenne conjecture
- Catalan surfaceCatalan surfaceIn geometry, a Catalan surface, named after the Belgian mathematician Eugène Charles Catalan, is a ruled surface all of whose rulings are parallel to a fixed plane. The vector equation of a Catalan surface is given by...
- Catalan's conjecture