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'''Ann Miller''' was born on [[April 12]], [[1923]] (some sources still indicate [[1919]]) and died on [[January 22]], [[2004]]. She was an American dancer, singer and actress, who was christened '''Johnnie Lucille Collier''' in [[Chireno, Texas]] (some sources cite [[Houston, Texas]]).
Etienne Bézout's father was Pierre Bézout who was a magistrate in the town of Nemours. One might have expected Etienne to follow the same career for his grandfather had also been a magistrate in Nemours. Etienne's mother was Hélène-Jeanne Filz.
As we have already indicated the family tradition almost demanded that Etienne follow in his father and grandfather's footsteps. However the remarkable mathematics of Leonard Euler proved stronger than his parents wishes for once Bézout had read Euler's works he wished to devote himself to mathematics. In 1756 he published a memoir Dynamique. In the following year he published Quantités différentielles and in 1758 Rectification des courbes. These letter two papers were investigation integration.
She was considered a child dance prodigy. She was given a contract with [[RKO]] allegedly at the tender age of thirteen (she had told them she was eighteen). She became famous for her roles in films such as [[Kiss Me, Kate]], [[Easter Parade]] and [[On the Town]]. Miller was famed for her speed in [[tap dancing]]; she claimed to be able to tap 500 times per minute.
In 1758 Bézout was appointed an adjoint in mechanics of the Académie des Sciences and, in the same year, as royal censor. He was appointed examiner of the Gardes de la Marine in 1763, the post being offered to him by the Duke of Choiseul. One important task that he was given in this role was to compose a textbook specially designed for teaching mathematics to the students.
Her father (from whom she would become estranged due to his infidelities to her mother) insisted on the name Johnnie because he had wanted a boy, but she was often called Annie. She took up dancing to help exercise her legs to help her [[rickets]]. Her film career effectively ended in [[1956]], but she remained active in the theatre. In [[1979]] she astounded audiences in the [[Broadway]] show [[Sugar Babies]]. In 1983 she won the [[Sarah Siddons Award]] for her work in [[Chicago]] theatre. In 2001 she took her last role as "Coco" in auteur director [[David Lynch]]'s movie [[Mulholland Drive (film)]].
Bézout is famed for the texbooks which came out of this assignment. The first was Cours de mathematiques à l'usage des gardes de la marine, a four volume work which appeared in 1764-67.
For her contribution to the motion picture industry, Ann Miller has a star on the [[Hollywood Walk of Fame]] at 6914 Hollywood Blvd.
In 1768 Camus, who was the examiner for the artillery, died. Bézout was appointed to succeed him becoming examiner of the Corps d'Artillerie. He began work on another mathematics textbook and as a result he produced Cours complet de mathematiques à l'usage de marine et de l'artillerie, a six volume work which appeared between 1770 and 1782. This was a very successful textbook and for many years it was the book which students hoping to enter the Ecole Polytechnique studied. Grabiner writes in [1]:-
She died at the age of 80 (or 84) from cancer that had spread to her lungs and was interred in the [[Holy Cross Cemetery]] in [[Culver City, California]].
The experience of teaching non-mathematicians shaped the style of the works: Bézout treated geometry before algebra, observing that beginners were not yet familiar enough with mathematical reasoning to understand the force of algebraic demonstrations, although they did appreciate proofs in geometry. He eschewed the frightening terms "axiom", "theorem", "scholium", and tried to avoid arguments that were too close and detailed.
As might be expected given this approach resulting the readership for whom Bézout intended his texts, his books came in for a certain amount of criticism for lacking rigour. However, despite this they were books which could be understood by those who needed to use mathematics and as a result were very popular and widely used. Their use spread beyond france for they were translated into English and used in North America. In particular Harvard University adopted them as calculus textbooks.
Returning to give more information about Bézout's career, we should note that he was promoted to associé in mechanics at the Académie des Sciences in 1768 and then further promoted to pensionnaire in 1770.
As we have indicated Bézout is famed for being a writer of textbooks but he is famed also for his work on algebra, in particular on equations. He was much occupied with his teaching duties after his 1763 appointments and he took these very seriously indeed. As a consequence he could devote relatively little time to research and he made a conscience decision to restrict the range of his work so that he could produce worthwhile results in a narrow order.
== Filmography ==
The way Bézout went about his research is interesting since still today it is a good approach for obtaining results. He attacked quite general problems, but since an attack was usually beyond what could be achieved with the mathematical knowledge then available, he attacked special cases of the general problems which he could solve. This approach often leads slowly to more and more understanding of the general case which may eventually become soluble. Bézout had a name for this approach to mathematics, namely the "method of simplifying assumptions".
* ''[[Anne of Green Gables]]'' (1934)
* ''[[The Good Fairy]]'' (1935)
* ''[[The Devil on Horseback]]'' (1936)
* ''[[New Faces of 1937]]'' (1937)
* ''[[The Life of the Party]]'' (1937)
* ''[[Stage Door]]'' (1937)
* ''[[Radio City Revels]]'' (1938)
* ''[[Having Wonderful Time]]'' (1938)
* ''[[You Can't Take It with You]]'' (1938)
* ''[[Room Service]]'' (1938)
* ''[[Tarnished Angel]]'' (1938)
* ''[[Too Many Girls]]'' (1940)
* ''[[Hit Parade of 1941]]'' (1940)
* ''[[Melody Ranch]]'' (1940)
* ''[[Time Out for Rhythm]]'' (1941)
* ''[[Meet the Stars: Stars Past and Present]]'' (1941) (short subject)
* ''[[Screen Snapshots: Series 21, No. 1]]'' (1941) (short subject)
* ''[[Go West, Young Lady]]'' (1941)
* ''[[True to the Army]]'' (1942)
* ''[[Priorities on Parade]]'' (1942)
* ''[[Reveille with Beverly]]'' (1943)
* ''[[What's Buzzin', Cousin?]]'' (1943)
* ''[[Hey, Rookie]]'' (1944)
* ''[[Jam Session]]'' (1944)
* ''[[Carolina Blues]]'' (1944)
* ''[[Eadie Was a Lady]]'' (1945)
* ''[[Eve Knew Her Apples]]'' (1945)
* ''[[The Thrill of Brazil]]'' (1946)
* ''[[Easter Parade]]'' (1948)
* ''[[The Kissing Bandit]]'' (1948)
* ''[[Mighty Manhattan, New York's Wonder City]]'' (1949) (short subject)
* ''[[On the Town]]'' (1949)
* ''[[Watch the Birdie]]'' (1950)
* ''[[Texas Carnival]]'' (1951)
* ''[[Two Tickets to Broadway]]'' (1951)
* ''[[Lovely to Look At]]'' (1952)
* ''[[Small Town Girl]]'' (1953)
* ''[[Calamity Jane]]'' (1953) (bit part)
* ''[[Kiss Me, Kate]]'' (1953)
* ''[[Deep in My Heart]]'' (1954)
* ''[[Hit the Deck]]'' (1955)
* ''[[The Opposite Sex]]'' (1956)
* ''[[The Great American Pastime]]'' (1956)
* ''[[Won Ton Ton, the Dog Who Saved Hollywood]]'' (1976)
* ''[[A Century of Cinema]]'' (1994) (documentary)
* ''[[That's Entertainment! III]]'' (1994)
* ''[[Mulholland Dr.]]'' (2001)
== External links ==
His first paper on the theory of equations Sur plusieurs classes d'equations de tous les degrés qui admettent une solution algébrique examined how a single equation in a single unknown could be attacked by writing it as two equations in two unknowns. He wrote in this paper:-
* {{imdb name|id=0587900|name=Ann Miller}}
* [http://newsvote.bbc.co.uk/2/hi/entertainment/3422589.stm BBC obituary]
[[Category:1923 births|Miller, Ann]]
It is known that a determinate equation can always be viewed as the result of two equations in two unknowns, when one of the unknowns is eliminated.
[[Category:2004 deaths|Miller, Ann]]
Of course on the face of it this does not help solve the equation but Bézout made the simplifying assumption that one of the two equations was of a particularly simple form. For example he considered the case when one of the two equations had only two terms, the term of degree n and a constant term. Already this paper had introduced the topic to which Bézout would make his most important contributions, namely methods of elimination to produce from a set of simultaneous equations, a single resultant equation in one of the unknowns.
[[Category:American actors|Miller, Ann]]
He also did important work on the use of determinants in solving equations. This appears in a paper Sur le degré des équations résultantes de l'évanouissement des inconnues which he published in 1764. As a result of the ideas in this paper for solving systems of simultaneous equations, Sylvester, in 1853, called the determinant of the matrix of coefficients of the equations the Bézoutiant.
[[Category:U.S. stage actors|Miller, Ann]]
[[Category:American film actors|Miller, Ann]]
[[Category:Hollywood Walk of Fame|Miller, Ann]]
[[Category:Female singers|Miller, Ann]]
[[Category:Tap dancers|Miller, Ann]]
[[Category:People from Texas|Miller, Ann]]
These and further papers published by Bézout in the theory of equations were gathered together in Théorie générale des équation algébraiques which was published in 1779. This work includes a result known as Bézout's theorem:-
[[de:Ann Miller]]
The degree of the final equation resulting from any number of complete equations in the same number of unknowns, and of any degrees, is equal to the product of the degrees of the equations.
[[fr:Ann Miller]]
By a complete equation Bézout meant one defined by a polynomial which contains terms of all possible products of the unknowns whose degree does not exceed that of the polynomial. One has to understand the problems that faced Bézout for he did not have our simple suffix notation to denote the unknowns by x1 , x2 , x3 , ... nor could he even label his equations with a suffix notation. Despite this Bézout, who was prepared to enter long and difficult algebraic manipulations, proved his theorem with just a little hand waving over an inductive argument.
[[nl:Ann Miller]]
In this work Bézout also gave the first satisfactory proof of a result of Maclaurin on the intersection of two algebraic curves.
[[sv:Ann Miller]]
Grabiner [1] tells us that:-
[Bézout] married early and happily; although he was reserved and somewhat sombre in society, those who knew him spoke of his great kindness and warm heart. By [1763] Bézout had become a father ...
After his death in 1730 a statue was erected in Nemours, the town of his birth, to commemorate his great achievements
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