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, structure, space, models, and change. History On ...

Biography

He was born at Épernon in France and studied at the

École Polytechnique École may refer to: * an elementary school in the French educational stages normally followed by secondary education establishments (collège and lycée) * École (river), a tributary of the Seine flowing in région Île-de-France * École, Savoi ...

Paris Paris () is the capital and most populous city of France, with an estimated population of 2,165,423 residents in 2019 in an area of more than 105 km² (41 sq mi), making it the 30th most densely populated city in the world in 2020. Si ...

under

Siméon Denis Poisson Baron Siméon Denis Poisson FRS FRSE (; 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, electri ...

. In the

War of the Sixth Coalition In the War of the Sixth Coalition (March 1813 – May 1814), sometimes known in Germany as the Wars of Liberation, a coalition of Austria, Prussia, Russia, Spain, the United Kingdom, Portugal, Sweden, and a number of German States defeated F ...

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, ...

. 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 Leonhard Sohncke (22 February 1842 Halle – 1 November 1897 in Munich) was a German mathematician who classified the 65 space groups in which chiral crystal structures form, called Sohncke groups. He was a professor of physics at the Technisch ...

) translated the original into German as ''Geschichte der geometrie, haupts achlich 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 Jakob Steiner (18 March 1796 – 1 April 1863) was a Swiss mathematician who worked primarily in geometry. Life Steiner was born in the village of Utzenstorf, Canton of Bern. At 18, he became a pupil of Heinrich Pestalozzi and afterwards st ...

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 Kinematics is a subfield of physics, developed in classical mechanics, that describes the motion of points, bodies (objects), and systems of bodies (groups of objects) without considering the forces that cause them to move. Kinematics, as a fiel ...

, 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 (abbreviation: AAA&S) 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, a ...

in 1864. In 1865 he was awarded the

Copley Medal The Copley Medal is an award given by the Royal Society, for "outstanding achievements in research in any branch of science". It alternates between the physical sciences or mathematics and the biological sciences. Given every year, the medal is t ...

. As described in ''A Treasury of Deception'', by Michael Farquhar (Peguin Books, 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 ( grc, Ἀλέξανδρος, Alexandros; 20/21 July 356 BC – 10/11 June 323 BC), commonly known as Alexander the Great, was a king of the ancient Greek kingdom of Macedon. He succeeded his father Philip II to ...

Aristotle Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatetic school of ...

, from

Cleopatra Cleopatra VII Philopator ( grc-gre, Κλεοπάτρα Φιλοπάτωρ}, "Cleopatra the father-beloved"; 69 BC10 August 30 BC) was Queen of the Ptolemaic Kingdom of Egypt from 51 to 30 BC, and its last active ruler.She was also a ...

Julius Caesar Gaius Julius Caesar (; ; 12 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 a civil war, an ...

, 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 his crucifixion and resurre ...

to a revived Lazarus, all in a fake medieval French. In 2004, the journal ''

Critical Inquiry ''Critical Inquiry'' is a quarterly peer-reviewed academic journal in the humanities published by the University of Chicago Press on behalf of the Department of English Language and Literature ( University of Chicago). While the topics and histo ...

'' 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. In 1986, Alexander Jones published a commentary on Book 7 of the ''Collection'' of

Pappus of Alexandria Pappus of Alexandria (; grc-gre, Πάππος ὁ Ἀλεξανδρεύς; AD) was one of the last great Greek mathematicians of antiquity known for his ''Synagoge'' (Συναγωγή) or ''Collection'' (), and for Pappus's hexagon theorem i ...

, 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 ...

: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 ''A'', ''B'', ''C'' and ''D'' on a line, t ...

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 (; grc-gre, Εὐκλείδης; 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 ...

'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 statutory land-grant research university based in Ithaca, New York. It is a member of the Ivy League. Founded in 1865 by Ezra Cornell and Andrew Dickson White, Cornell was founded with the intention to tea ...

. * M. Chasles (1865
Traité des sections coniques
Gauthier-Villars, from

University of Michigan , mottoeng = "Arts, Knowledge, Truth" , former_names = Catholepistemiad, or University of Michigania (1817–1821) , budget = $10.3 billion (2021) , endowment = $17 billion (2021)As o ...

. * M. Chasles (1852, 1880
Traité de Géométrie Supérieure
Gauthier-Villars, from

Google Google LLC () is an American Multinational corporation, multinational technology company focusing on Search Engine, search engine technology, online advertising, cloud computing, software, computer software, quantum computing, e-commerce, ar ...

Notes

References

* * {{DEFAULTSORT:Chasles, Michel 1793 births 1880 deaths Burials at Père Lachaise Cemetery 19th-century French mathematicians French geometers French historians of mathematics University of Paris faculty Recipients of the Copley Medal French Roman Catholics 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

Biography

Publications

See also

Notes

References