Michel Floréal Chasles (; 15 November 1793 – 18 December 1880) was a French
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
.
Biography
He was born at
Épernon in France and studied at the
École Polytechnique
(, ; also known as Polytechnique or l'X ) is a ''grande école'' located in Palaiseau, France. It specializes in science and engineering and is a founding member of the Polytechnic Institute of Paris.
The school was founded in 1794 by mat ...
in
Paris
Paris () is the Capital city, capital and List of communes in France with over 20,000 inhabitants, largest city of France. With an estimated population of 2,048,472 residents in January 2025 in an area of more than , Paris is the List of ci ...
under
Siméon Denis Poisson
Baron Siméon Denis Poisson (, ; ; 21 June 1781 – 25 April 1840) was a French mathematician and physicist who worked on statistics, complex analysis, partial differential equations, the calculus of variations, analytical mechanics, electricity ...
. In the
War of the Sixth Coalition
In the War of the Sixth Coalition () (December 1812 – May 1814), sometimes known in Germany as the Wars of Liberation (), a coalition of Austrian Empire, Austria, Kingdom of Prussia, Prussia, Russian Empire, Russia, History of Spain (1808– ...
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 the book ''Aperçu historique sur l'origine et le développement des méthodes en géométrie'' ("Historical view of the origin and development of methods in geometry"), a study of the method of reciprocal
polars in
projective geometry
In mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations. This means that, compared to elementary Euclidean geometry, projective geometry has a different setting (''p ...
. 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 this book was published in 1875. In 1839, Ludwig Adolph Sohncke (the father of
Leonhard Sohncke) translated the original into German as ''Geschichte der geometrie, hauptsachlich mit bezug auf die neueren methoden''. Shortly thereafter, in 1841,
Charles Graves published an English version as ''Two Geometrical Memoirs on the General Properties of Cones of the Second Degree and on the Spherical Conics'', adding a significant amount of original material.
Jakob Steiner had proposed
Steiner's conic 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's theorem). In
kinematics
In physics, kinematics studies the geometrical aspects of motion of physical objects independent of forces that set them in motion. Constrained motion such as linked machine parts are also described as kinematics.
Kinematics is concerned with s ...
, Chasles's description of a Euclidean motion in space
as screw displacement was seminal to the development of the theories of
dynamics of
rigid bodies.
Chasles was elected a Foreign Honorary Member of the
American Academy of Arts and Sciences
The American Academy of Arts and Sciences (The Academy) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and other ...
in 1864.
In 1865 he was awarded the
Copley Medal
The Copley Medal is the most prestigious award of the Royal Society of the United Kingdom, conferred "for sustained, outstanding achievements in any field of science". The award alternates between the physical sciences or mathematics and the bio ...
.
As described in ''A Treasury of Deception'', by Michael Farquhar (
Penguin Books
Penguin Books Limited is a Germany, German-owned English publishing, publishing house. It was co-founded in 1935 by Allen Lane with his brothers Richard and John, as a line of the publishers the Bodley Head, only becoming a separate company the ...
, 2005), between 1861 and 1869 Chasles purchased some of the 27,000 forged letters from Frenchman
Denis Vrain-Lucas. Included in this trove were letters from
Alexander the Great
Alexander III of Macedon (; 20/21 July 356 BC – 10/11 June 323 BC), most commonly known as Alexander the Great, was a king of the Ancient Greece, ancient Greek kingdom of Macedonia (ancient kingdom), Macedon. He succeeded his father Philip ...
to
Aristotle
Aristotle (; 384–322 BC) was an Ancient Greek philosophy, Ancient Greek philosopher and polymath. His writings cover a broad range of subjects spanning the natural sciences, philosophy, linguistics, economics, politics, psychology, a ...
, from
Cleopatra
Cleopatra VII Thea Philopator (; The name Cleopatra is pronounced , or sometimes in both British and American English, see and respectively. Her name was pronounced in the Greek dialect of Egypt (see Koine Greek phonology). She was ...
to
Julius Caesar
Gaius Julius Caesar (12 or 13 July 100 BC – 15 March 44 BC) was a Roman general and statesman. A member of the First Triumvirate, Caesar led the Roman armies in the Gallic Wars before defeating his political rival Pompey in Caesar's civil wa ...
, and from
Mary Magdalene
Mary Magdalene (sometimes called Mary of Magdala, or simply the Magdalene or the Madeleine) was a woman who, according to the four canonical gospels, traveled with Jesus as one of his followers and was a witness to crucifixion of Jesus, his cr ...
to a revived
Lazarus, all in a fake medieval French. In 2004, the journal ''
Critical Inquiry'' published a recently "discovered" 1871 letter written by Vrain-Lucas (from prison) to Chasles, conveying Vrain-Lucas's perspective on these events, itself an invention.
Modern assessment of contribution
In 1986, Alexander Jones published a commentary on Book 7 of the ''Collection'' of
Pappus of Alexandria
Pappus of Alexandria (; ; AD) was a Greek mathematics, Greek mathematician of late antiquity known for his ''Synagoge'' (Συναγωγή) or ''Collection'' (), and for Pappus's hexagon theorem in projective geometry. Almost nothing is known a ...
, which Chasles had referred to in his history of geometric methods. Jones makes these comments about Chasles, Pappus and Euclid:
[Alexander Jones (1986) ''Book 7 of the Collection'', part 1: introduction, text, translation , part 2: commentary, index, figures , ]Springer-Verlag
Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.
Originally founded in 1842 in ...
: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-ratio
In geometry, the cross-ratio, also called the double ratio and anharmonic ratio, is a number associated with a list of four collinear points, particularly points on a projective line. Given four points , , , on a line, their cross ratio is defin ...
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
Euclid
Euclid (; ; BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the '' Elements'' treatise, which established the foundations of geometry that largely domina ...
's, even if we cannot now tell which they are.
Chasles's name is one of the
72 names inscribed on the Eiffel Tower.
Publications
*
* M. Chasles (1837
Aperçu historique sur l'origine et le développement des méthodes en géométrie originally published by Hayez in Bruxelles, now from
archive.org.
* M. Chasles (1841
Two geometrical memoirs on the general properties of cones of the second degree, and other spherical conics Charles Graves translator, originally published in Dublin, now from
Cornell University
Cornell University is a Private university, private Ivy League research university based in Ithaca, New York, United States. The university was co-founded by American philanthropist Ezra Cornell and historian and educator Andrew Dickson W ...
.
* M. Chasles (1852, 1880
Traité de Géométrie Supérieure Gauthier-Villars.
* M. Chasles (1865
Traité des sections coniques Gauthier-Villars, from
University of Michigan
The University of Michigan (U-M, U of M, or Michigan) is a public university, public research university in Ann Arbor, Michigan, United States. Founded in 1817, it is the oldest institution of higher education in the state. The University of Mi ...
.
See also
*
Chasles–Cayley–Brill formula
*
Chasles's theorem (disambiguation)
*Asteroid
18510 Chasles
Notes
References
*
*
{{DEFAULTSORT:Chasles, Michel
1793 births
1880 deaths
Burials at Père Lachaise Cemetery
19th-century French mathematicians
French geometers
French historians of mathematics
Academic staff of the University of Paris
Recipients of the Copley Medal
École Polytechnique alumni
Members of the French Academy of Sciences
Lycée Louis-le-Grand alumni
Fellows of the American Academy of Arts and Sciences
Foreign members of the Royal Society
Foreign associates of the National Academy of Sciences
Corresponding members of the Saint Petersburg Academy of Sciences
French military personnel of the Napoleonic Wars