Michel Chasles
Encyclopedia
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. After the war, he gave up on a career as an engineer or stockbroker in order to pursue his mathematical studies.
In 1837 he published his Historical view of the origin and development of methods in geometry, a study of the method of reciprocal polars
in projective geometry
. The work gained him considerable fame and respect and he was appointed Professor at the École Polytechnique in 1841, then he was awarded a chair at the Sorbonne
in 1846. A second edition of his book was published in 1875, and Leonhard Sohncke translated the work into German.
Jakob Steiner
had proposed the problem of enumerating the number of conic sections tangent to each of five given conics, and had answered it incorrectly. Chasles developed a theory of characteristics that enabled the correct enumeration of the conics (there are 3264) (see enumerative geometry
). He established several important theorems (all called Chasles' theorem). That on solid body kinematics was seminal for understanding their motions, and hence to the development of the theories of dynamics of rigid bodies.
In 1865 he was awarded the Copley Medal
.
As described in A Treasury of Deception, by Michael Farquhar (Peguin Books, 2005), between 1861 and 1869 Chasles purchased over 27,000 forged letters from Frenchman Denis Vrain-Lucas. Included in this trove were letters from Alexander the Great to Aristotle
, from Cleopatra to Julius Caesar
, and from Mary Magdalene
to a revived Lazarus
, all in a fake maedieval French. In 2004, the journal Critical Inquiry published a recently uncovered 1871 letter (translated by Northwestern University historian of science Ken Alder) written by Vrain-Lucas (from prison) to Chasles, conveying Vrain-Lucas's perspectives on these events.
In 1986, Alexander Jones published a commentary on Book 7 of the Collection of Pappus of Alexandria
, which Chasles had referred to in his history of geometric methods. Jones makes these comments about Chasles, Pappus and Euclid:
Chasles' name is one of 72 that appears on the Eiffel Tower
.
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...
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 at Épernon
Épernon
Épernon is a commune in the Eure-et-Loir department in the Centre region in northern France. It lies some 27 km northeast of Chartres, at the confluence of the Drouette and the Guesle.-History:...
in France and studied at the 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
Paris
Paris is the capital and largest city in France, situated on the river Seine, in northern France, at the heart of the Île-de-France region...
under Siméon Denis Poisson
Siméon Denis Poisson
Siméon Denis Poisson , was a French mathematician, geometer, and physicist. He however, was the final leading opponent of the wave theory of light as a member of the elite l'Académie française, but was proven wrong by Augustin-Jean Fresnel.-Biography:...
. In the War of the Sixth Coalition
War of the Sixth Coalition
In the War of the Sixth Coalition , a coalition of Austria, Prussia, Russia, the United Kingdom, Portugal, Sweden, Spain and a number of German States finally defeated France and drove Napoleon Bonaparte into exile on Elba. After Napoleon's disastrous invasion of Russia, the continental powers...
he was drafted to fight in the defence of Paris in 1814. After the war, he gave up on a career as an engineer or stockbroker in order to pursue his mathematical studies.
In 1837 he published his Historical view of the origin and development of methods in geometry, a study of the method of reciprocal polars
Pole and polar
In geometry, the terms pole and polar are used to describe a point and a line that have a unique reciprocal relationship with respect to a given conic section...
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...
. The work gained him considerable fame and respect and he was appointed Professor at the École Polytechnique in 1841, then he was awarded a chair at the Sorbonne
University of Paris
The University of Paris was a university located in Paris, France and one of the earliest to be established in Europe. It was founded in the mid 12th century, and officially recognized as a university probably between 1160 and 1250...
in 1846. A second edition of his book was published in 1875, and Leonhard Sohncke translated the work into German.
Jakob Steiner
Jakob Steiner
Jakob Steiner was a Swiss mathematician who worked primarily in geometry.-Personal and professional life:...
had proposed the problem of enumerating the number of conic sections tangent to each of five given conics, and had answered it incorrectly. Chasles developed a theory of characteristics that enabled the correct enumeration of the conics (there are 3264) (see enumerative geometry
Enumerative geometry
In mathematics, enumerative geometry is the branch of algebraic geometry concerned with counting numbers of solutions to geometric questions, mainly by means of intersection theory.-History:...
). He established several important theorems (all called Chasles' theorem). That on solid body kinematics was seminal for understanding their motions, and hence to the development of the theories of dynamics of rigid bodies.
In 1865 he was awarded the Copley Medal
Copley Medal
The Copley Medal is an award given by the Royal Society of London for "outstanding achievements in research in any branch of science, and alternates between the physical sciences and the biological sciences"...
.
As described in A Treasury of Deception, by Michael Farquhar (Peguin Books, 2005), between 1861 and 1869 Chasles purchased over 27,000 forged letters from Frenchman Denis Vrain-Lucas. Included in this trove were letters from Alexander the Great to Aristotle
Aristotle
Aristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...
, from Cleopatra to Julius Caesar
Julius Caesar
Gaius Julius Caesar was a Roman general and statesman and a distinguished writer of Latin prose. He played a critical role in the gradual transformation of the Roman Republic into the Roman Empire....
, and from Mary Magdalene
Mary Magdalene
Mary Magdalene was one of Jesus' most celebrated disciples, and the most important woman disciple in the movement of Jesus. Jesus cleansed her of "seven demons", conventionally interpreted as referring to complex illnesses...
to a revived Lazarus
Lazarus of Bethany
Lazarus of Bethany, also known as Saint Lazarus or Lazarus of the Four Days, is the subject of a prominent miracle attributed to Jesus in the Gospel of John, in which Jesus restores him to life four days after his death...
, all in a fake maedieval French. In 2004, the journal Critical Inquiry published a recently uncovered 1871 letter (translated by Northwestern University historian of science Ken Alder) written by Vrain-Lucas (from prison) to Chasles, conveying Vrain-Lucas's perspectives on these events.
In 1986, Alexander Jones published a commentary on Book 7 of the Collection of Pappus of Alexandria
Pappus of Alexandria
Pappus of Alexandria was one of the last great Greek mathematicians of Antiquity, known for his Synagoge or Collection , and for Pappus's Theorem in projective geometry...
, which Chasles had referred to in his history of geometric methods. Jones makes these comments about Chasles, Pappus and Euclid:
- Chasles's contribution to our comprehension of the Porisms tends to be obscured by the inherent unreasonableness of his claim to have restored substantially the contents of Euclid's book on the basis of the meagre data of Pappus and Proclus...one still turns to Chasles for the first appreciation of the interest in the Porisms from the point of view of modern geometry. Above all, he was the first to notice the recurrence of cross-ratioCross-ratioIn geometry, the cross-ratio, also called double ratio and anharmonic ratio, is a special number associated with an ordered quadruple of collinear points, particularly points on a projective line...
s and harmonic ratios in the lemmas, and because these concepts suffuse most of his restoration, it is probable that many of his inventions coincide with some of EuclidEuclidEuclid , fl. 300 BC, also known as Euclid of Alexandria, was a Greek mathematician, often referred to as the "Father of Geometry". He was active in Alexandria during the reign of Ptolemy I...
's, even if we cannot now tell which they are.
Chasles' name is one of 72 that appears on the Eiffel Tower
Eiffel Tower
The Eiffel Tower is a puddle iron lattice tower located on the Champ de Mars in Paris. Built in 1889, it has become both a global icon of France and one of the most recognizable structures in the world...
.