Joseph Diaz Gergonne
Encyclopedia
Joseph Diaz Gergonne was a French mathematician
and logician.
and restore Louis XVI to full power. He saw action in the major battle of Valmy
on 20 September 1792. He then returned to civilian life but soon was called up again and took part in the 1794 French invasion of Spain.
In 1795, Gergonne and his regiment were sent to Nîmes
. At this point, he made a definitive transition to civilian life by taking up the chair of "transcendental mathematics" at the new École Centrale. He came under the influence of Gaspard Monge
, the Director of the new École Polytechnique
in Paris.
In 1810, in response to difficulties he encountered in trying to publish his work, Gergonne founded his own mathematics journal, officially named the Annales de mathématiques pures et appliquées but generally referred to as the Annales de Gergonne. The most common subject of articles in his journal was geometry
, Gergonne's specialty. Over a period of 22 years, the Annales de Gergonne published about 200 articles by Gergonne himself, and other articles by many distinguished mathematicians, including Poncelet
, Servois, Bobillier, Steiner
, Plücker
, Chasles
, Brianchon, Dupin, Lamé, even Galois
.
Gergonne was appointed to the chair of astronomy at the University of Montpellier in 1816. In 1830, he was appointed Rector of the University of Montpellier, at which time he ceased publishing his journal. He retired in 1844.
. In a series of papers beginning in 1810, he discovered the principle of duality in projective geometry
, by noticing that every theorem in the plane connecting points and lines corresponds to another theorem in which points and lines are interchanged, provided that the theorem embodied no metrical notions. In 1816, he devised an elegant solution to the problem of Apollonius
: find a circle which touches three given circles.
In 1813, Gergonne wrote the prize-winning essay for the Bordeaux Academy, Methods of synthesis and analysis in mathematics, unpublished to this day and known only via a summary. The essay is very revealing of Gergonne's philosophical ideas. He called for the abandonment of the words analysis and synthesis, claiming they lacked clear meanings. Surprisingly for a geometer, he suggested that algebra is more important than geometry, at a time when algebra
consisted almost entirely of the elementary algebra of the real field
. He predicted that one day quasi-mechanical methods would be used to discover new results.
In 1815, Gergonne wrote the first paper on the optimal design
of experiments
for polynomial regression
. According to S. M. Stigler, Gergonne is the pioneer of optimal design
as well as response surface methodology
.
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....
and logician.
Life
In 1791, Gergonne enlisted in the French army as a captain. That army was undergoing rapid expansion because the French government feared a foreign invasion intended to undo the French RevolutionFrench Revolution
The French Revolution , sometimes distinguished as the 'Great French Revolution' , was a period of radical social and political upheaval in France and Europe. The absolute monarchy that had ruled France for centuries collapsed in three years...
and restore Louis XVI to full power. He saw action in the major battle of Valmy
Valmy
Valmy is a commune in the Marne department in north-eastern France.-Geography:The town stands on the west flank of the Argonne massif, mid-way between Verdun and Paris, near Vouziers.-History:...
on 20 September 1792. He then returned to civilian life but soon was called up again and took part in the 1794 French invasion of Spain.
In 1795, Gergonne and his regiment were sent to Nîmes
Nîmes
Nîmes is the capital of the Gard department in the Languedoc-Roussillon region in southern France. Nîmes has a rich history, dating back to the Roman Empire, and is a popular tourist destination.-History:...
. At this point, he made a definitive transition to civilian life by taking up the chair of "transcendental mathematics" at the new École Centrale. He came under the influence of Gaspard Monge
Gaspard Monge
Gaspard Monge, Comte de Péluse was a French mathematician, revolutionary, and was inventor of descriptive geometry. During the French Revolution, he was involved in the complete reorganization of the educational system, founding the École Polytechnique...
, the Director of the new 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...
in Paris.
In 1810, in response to difficulties he encountered in trying to publish his work, Gergonne founded his own mathematics journal, officially named the Annales de mathématiques pures et appliquées but generally referred to as the Annales de Gergonne. The most common subject of articles in his journal was 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 ....
, Gergonne's specialty. Over a period of 22 years, the Annales de Gergonne published about 200 articles by Gergonne himself, and other articles by many distinguished mathematicians, including Poncelet
Poncelet
The poncelet is an obsolete unit of power, once used in France and replaced by cheval vapeur . The unit was named after Jean-Victor Poncelet....
, Servois, Bobillier, Steiner
Steiner
-Surname:*Achim Steiner , German expert in environmental politics*Anton Steiner , Austrian former alpine skier*Ben Steiner , Major League Baseball player*Cecil C...
, Plücker
Plucker
Plucker is an offline Web and free e-book reader for Palm OS based handheld devices, Windows Mobile devices and other PDAs. Plucker contains POSIX tools, scripts and "conduits" which work on Unix, Linux, Mac OS X, and Microsoft Windows...
, Chasles
Michel Chasles
Michel Floréal Chasles was a French mathematician.He was born at Épernon in France and studied at the École Polytechnique in Paris under Siméon Denis Poisson. In the War of the Sixth Coalition he was drafted to fight in the defence of Paris in 1814...
, Brianchon, Dupin, Lamé, even Galois
Évariste Galois
Évariste Galois was a French mathematician born in Bourg-la-Reine. While still in his teens, he was able to determine a necessary and sufficient condition for a polynomial to be solvable by radicals, thereby solving a long-standing problem...
.
Gergonne was appointed to the chair of astronomy at the University of Montpellier in 1816. In 1830, he was appointed Rector of the University of Montpellier, at which time he ceased publishing his journal. He retired in 1844.
Work
Gergonne was the first mathematician to employ the word polarPolar coordinate system
In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a fixed point and an angle from a fixed direction....
. In a series of papers beginning in 1810, he discovered the principle of duality in projective geometry
Projective geometry
In mathematics, projective geometry is the study of geometric properties that are invariant under projective transformations. This means that, compared to elementary geometry, projective geometry has a different setting, projective space, and a selective set of basic geometric concepts...
, by noticing that every theorem in the plane connecting points and lines corresponds to another theorem in which points and lines are interchanged, provided that the theorem embodied no metrical notions. In 1816, he devised an elegant solution to the problem of Apollonius
Problem of Apollonius
In Euclidean plane geometry, Apollonius' problem is to construct circles that are tangent to three given circles in a plane . Apollonius of Perga posed and solved this famous problem in his work ; this work has been lost, but a 4th-century report of his results by Pappus of Alexandria has survived...
: find a circle which touches three given circles.
In 1813, Gergonne wrote the prize-winning essay for the Bordeaux Academy, Methods of synthesis and analysis in mathematics, unpublished to this day and known only via a summary. The essay is very revealing of Gergonne's philosophical ideas. He called for the abandonment of the words analysis and synthesis, claiming they lacked clear meanings. Surprisingly for a geometer, he suggested that algebra is more important than geometry, at a time when algebra
Abstract algebra
Abstract algebra is the subject area of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras...
consisted almost entirely of the elementary algebra of the real field
Real field
Real field may refer to:* Real numbers, the numbers that can be represented by infinite decimals* Formally real field, an algebraic field that has the so-called "real" property* Realfield, a spoof of Garfield...
. He predicted that one day quasi-mechanical methods would be used to discover new results.
In 1815, Gergonne wrote the first paper on the optimal design
Optimal design
Optimal designs are a class of experimental designs that are optimal with respect to some statistical criterion.In the design of experiments for estimating statistical models, optimal designs allow parameters to be estimated without bias and with minimum-variance...
of experiments
Design of experiments
In general usage, design of experiments or experimental design is the design of any information-gathering exercises where variation is present, whether under the full control of the experimenter or not. However, in statistics, these terms are usually used for controlled experiments...
for polynomial regression
Polynomial regression
In statistics, polynomial regression is a form of linear regression in which the relationship between the independent variable x and the dependent variable y is modeled as an nth order polynomial...
. According to S. M. Stigler, Gergonne is the pioneer of optimal design
Optimal design
Optimal designs are a class of experimental designs that are optimal with respect to some statistical criterion.In the design of experiments for estimating statistical models, optimal designs allow parameters to be estimated without bias and with minimum-variance...
as well as response surface methodology
Response surface methodology
In statistics, response surface methodology explores the relationships between several explanatory variables and one or more response variables. The method was introduced by G. E. P. Box and K. B. Wilson in 1951. The main idea of RSM is to use a sequence of designed experiments to obtain an...
.
Quote
- "It is not possible to feel satisfied at having said the last word about some theory as long as it cannot be explained in a few words to any passer-by encountered in the street. "
External links
- Biography in the MacTutor History of Mathematics archive: Joseph Gergonne.