Who was Adrien-Marie Legendre and what were his primary fields of contribution?

Adrien-Marie Legendre (1752-1833) was a French mathematician renowned for his significant contributions across several mathematical fields. His work notably advanced areas such as number theory, elliptic functions, and the method of least squares. Concepts like Legendre polynomials and the Legendre transformation are named in his honor, reflecting the importance of his research in mathematics and its applications.

When was Adrien-Marie Legendre born and when did he die?

Adrien-Marie Legendre was born on September 18, 1752, and passed away on January 9, 1833.

What are some of the mathematical concepts named after Adrien-Marie Legendre?

Several important mathematical concepts bear Adrien-Marie Legendre's name, including the Legendre polynomials, the Legendre transformation, the Legendre symbol, and Legendre's constant. His work also contributed to areas like elliptic functions and number theory.

How did Legendre's work on the method of least squares compare to Carl Friedrich Gauss's?

Adrien-Marie Legendre was the first to officially publish on the method of least squares in 1806, applying it to the paths of comets. However, the text notes that Carl Friedrich Gauss had independently discovered this method prior to Legendre's publication.

What mathematical symbol is attributed to Adrien-Marie Legendre?

Adrien-Marie Legendre is credited with introducing the symbol ∂, which is commonly used in calculus, particularly for partial derivatives.

What was Legendre's educational background?

Legendre received his education at the Collège Mazarin in Paris, where he successfully defended his thesis in physics and mathematics in 1770.

Where did Legendre teach mathematics during his career?

Adrien-Marie Legendre taught mathematics at the École Militaire in Paris from 1775 to 1780 and at the École Normale starting in 1795. He was also associated with the Bureau des Longitudes.

What recognition did Legendre receive from the Berlin Academy in 1782?

In 1782, the Berlin Academy awarded Legendre a prize for his treatise on projectiles in resistant media, a work that also brought him to the attention of the mathematician Lagrange.

When did Legendre become a member of the Académie des sciences and the Royal Society?

Legendre became an adjoint member of the Académie des sciences in 1783 and an associate member in 1785. He was elected a Fellow of the Royal Society in 1789.

What was Legendre's role in the Anglo-French Survey?

Adrien-Marie Legendre participated in the Anglo-French Survey conducted between 1784 and 1790. His contribution involved assisting in the precise calculation of the distance between the Paris Observatory and the Royal Greenwich Observatory using trigonometry. During this survey, he visited Dover and London and met William Herschel.

How did the French Revolution affect Legendre financially?

During the French Revolution, in 1793, Adrien-Marie Legendre lost his private fortune.

What positions did Legendre hold within the French scientific institutions after the Revolution?

Following the French Revolution, Legendre became one of the six members of the mathematics section of the reconstituted Académie des Sciences (renamed the Institut National des Sciences et des Arts) in 1795. After Napoleon reorganized the Institut National in 1803, Legendre became a member of its Geometry section. He also served as a mathematics examiner for graduating artillery students at the École Militaire and for the École Polytechnique.

Why was Legendre's pension stopped in 1824?

Legendre's pension from the École Militaire was stopped in 1824 because he refused to vote for the government's candidate at the Institut National.

When was Legendre made an officer of the Légion d'Honneur?

Adrien-Marie Legendre was made an officer of the Légion d'Honneur in 1831.

Where is Adrien-Marie Legendre buried?

Adrien-Marie Legendre is buried in the village of Auteuil, Paris, next to his wife, Marguerite-Claudine Couhin.

How is Adrien-Marie Legendre commemorated on the Eiffel Tower?

Adrien-Marie Legendre is honored as one of the 72 prominent French scientists whose names are inscribed on the Eiffel Tower.

On whose work did Abel build regarding elliptic functions, and whose work did Legendre's complete in statistics and number theory?

Niels Henrik Abel built upon Legendre's work concerning elliptic functions. Additionally, some of Carl Friedrich Gauss's contributions in statistics and number theory are noted as completing Legendre's earlier work in those fields.

What is the method of least squares, and where is it applied?

The method of least squares is a statistical technique used to find the best fit line or curve for a series of data points. It has broad applications in fields such as linear regression, signal processing, statistics, and curve fitting.

What was Legendre's major work published between 1811 and 1819, and what did it introduce?

Legendre's major work published in three volumes between 1811 and 1819 was titled *Exercices de Calcul Intégral*. This work introduced the fundamental properties of elliptic integrals, beta functions, and gamma functions, including the symbol Γ and its normalization Γ(n+1) = n!. It also explored applications in mechanics, such as the Earth's rotation and the attraction of ellipsoids.

What specific mathematical functions and symbols did Legendre introduce or normalize in his *Exercices de Calcul Intégral*?

In his three-volume work *Exercices de Calcul Intégral*, Legendre introduced the basic properties of elliptic integrals, beta functions, and gamma functions. He also introduced the symbol Γ and normalized it such that Γ(n+1) = n!.

For which exponent of Fermat's Last Theorem did Legendre provide a proof, and who else proved it?

In 1830, Adrien-Marie Legendre provided a proof for Fermat's Last Theorem for the exponent n=5. Peter Gustav Lejeune Dirichlet also independently proved the theorem for n=5 in 1828.

What conjecture in number theory did Legendre make that was later proved by Gauss?

In the field of number theory, Legendre conjectured the quadratic reciprocity law, which was later proved by Carl Friedrich Gauss.

What is the Legendre symbol named after him, and what area of mathematics did it relate to?

The Legendre symbol is named after Adrien-Marie Legendre and is related to number theory, specifically in the context of quadratic reciprocity.

What conjecture did Legendre make in 1798 regarding prime numbers, and who later proved it?

In 1798, Legendre conjectured the prime number theorem, which posits a relationship concerning the distribution of prime numbers. This conjecture was rigorously proved much later, in 1896, by Jacques Hadamard and Charles Jean de la Vallée Poussin.

How did Legendre's work on elliptic functions contribute to the field, and what was needed to fully solve the problem?

Legendre made significant contributions to the study of elliptic functions, including the classification of elliptic integrals. However, it was Niels Henrik Abel's study of the inverses of Carl Gustav Jakob Jacobi's functions that ultimately provided a complete solution to the problems Legendre had explored.

What is the Legendre transformation used for in classical mechanics and thermodynamics?

The Legendre transformation is a mathematical tool used in classical mechanics to convert the Lagrangian formulation into the Hamiltonian formulation. In thermodynamics, it is employed to derive quantities like enthalpy and the Helmholtz and Gibbs free energies from the internal energy.

What are Legendre polynomials, and where do they find applications?

Legendre polynomials are solutions to Legendre's differential equation. They are frequently encountered and applied in various areas of physics and engineering, such as in the study of electrostatics.

What is Adrien-Marie Legendre best known for in terms of his publications, and how did it differ from Euclid's work?

Adrien-Marie Legendre is perhaps best known for his publication *Éléments de géométrie*, released in 1794. This textbook served as a primary resource on geometry for approximately a century. Legendre's approach involved significantly rearranging and simplifying the propositions found in Euclid's *Elements* to create a more effective and accessible textbook for students.

How long was Legendre's *Éléments de géométrie* considered a leading textbook?

Legendre's *Éléments de géométrie* was considered the leading elementary textbook on the subject for about 100 years after its publication in 1794.

What honor did Legendre receive from the American Academy of Arts and Sciences in 1832?

In 1832, Adrien-Marie Legendre was made a Foreign Honorary Member of the American Academy of Arts and Sciences.

What celestial body features a crater named after Legendre?

A crater on the Moon is named Legendre in honor of the mathematician.

What astronomical body, specifically an asteroid, is named 26950 Legendre?

The main-belt asteroid designated 26950 Legendre is named in his honor.

Besides the Eiffel Tower inscription, what other public recognition did Legendre receive in Paris?

A street in Paris' 17th Arrondissement is named after Adrien-Marie Legendre, recognizing his contributions.

What was the title of Legendre's 1782 prize-winning essay from the Berlin Academy?

The title of Legendre's 1782 essay, which won a prize from the Berlin Academy, was *Recherches sur la trajectoire des projectiles dans les milieux résistants* (Research on the trajectory of projectiles in resistant media).

What are the titles and publication years of Legendre's major books mentioned in the text?

Adrien-Marie Legendre authored several significant books, including *Éléments de géométrie* (1794), *Essai sur la Théorie des Nombres* (1797-8, with later editions), *Nouvelles Méthodes pour la Détermination des Orbites des Comètes* (1805), *Exercices de Calcul Intégral* (1811, 1817, 1819), and *Traité des Fonctions Elliptiques* (1825, 1826, 1830).

Which of Legendre's publications introduced the basic properties of elliptic integrals, beta functions, and the gamma function symbol?

The introduction of the basic properties of elliptic integrals, beta functions, and the gamma function symbol (Γ) occurred in the first volume of Legendre's major work, *Exercices de Calcul Intégral*, published in 1811.

What specific mathematical topic was addressed in Legendre's 1783 memoir published in the *Histoire de l'Académie Royale des Sciences*?

Legendre's 1783 memoir, published in the *Histoire de l'Académie Royale des Sciences*, was titled *Sur l'attraction des Sphéroïdes homogènes* (On the attraction of homogeneous spheroids) and dealt with work related to Legendre polynomials.

Which of Legendre's memoirs, published in the *Mémoires présentés par divers Savants*, dealt with the method of least squares and the attraction of ellipsoids?

In 1819, Legendre published two memoirs in *Mémoires présentés par divers Savants*: one titled *Méthode des moindres carrés pour trouver le milieu le plus probable entre les résultats de différentes observations* (Method of least squares for finding the most probable mean between the results of different observations) and another titled *Mémoire sur l'attraction des ellipsoïdes homogènes* (Memoir on the attraction of homogeneous ellipsoids).

What topic was covered in Legendre's 1823 memoir published in *Mémoires présentés par divers Savants*?

Legendre's 1823 memoir, published in *Mémoires présentés par divers Savants*, was titled *Recherches sur quelques objets d'Analyse indéterminée et particulièrement sur le théorème de Fermat* (Research on some objects of indeterminate analysis and particularly on Fermat's theorem).

Whose portrait was mistakenly used for Adrien-Marie Legendre for nearly two centuries?

For approximately two centuries, the portrait of the French politician Louis Legendre (1752–1797) was mistakenly identified as that of the mathematician Adrien-Marie Legendre. This error persisted until 2005 when it was corrected.

When was the error concerning Legendre's portrait discovered?

The error where the portrait of politician Louis Legendre was mistakenly used for the mathematician Adrien-Marie Legendre was discovered in 2005.

What is the name of the 1820 book containing caricatures of members of the Institut de France, which includes a portrait of Legendre?

The 1820 book containing caricatures of members of the Institut de France, which includes a portrait of Legendre, is titled *Album de 73 portraits-charge aquarellés des membres de I'Institut*.

Who was the artist responsible for the watercolor caricatures that include a portrait of Legendre?

The French artist Julien-Léopold Boilly was responsible for the watercolor caricatures that include a portrait of Adrien-Marie Legendre.

What are the two known portraits of Adrien-Marie Legendre mentioned in the text?

The text mentions two known portraits of Adrien-Marie Legendre: one is found in Julien-Léopold Boilly's 1820 book *Album de 73 portraits-charge aquarellés des membres de I'Institut*, and the other is from the book *Le Panthéon scientifique de la tour Eiffel*.

What is the name of the algorithm developed jointly with Gauss that is named after both mathematicians?

The Gauss–Legendre algorithm is named after both Carl Friedrich Gauss and Adrien-Marie Legendre.

What is the name of the conjecture in number theory attributed to Legendre?

The conjecture in number theory attributed to Adrien-Marie Legendre is known as Legendre's conjecture.

What specific theorem related to spherical triangles is named after Legendre?

Legendre's theorem on spherical triangles is a theorem named after Adrien-Marie Legendre.

What is the name of the mathematical concept related to prime numbers that Legendre developed, distinct from his conjecture?

Distinct from his conjecture on prime numbers, Adrien-Marie Legendre also developed the Legendre sieve, a method related to the distribution and identification of prime numbers.

What is described as the only authenticated portrait of Adrien-Marie Legendre, and who created it?

The text describes a watercolor caricature by Julien-Léopold Boilly as the only authenticated portrait of Adrien-Marie Legendre. This artwork is part of a larger collection of caricatures of members of the Institut de France.

What is the nature of the portrait shown in the 'Legendre.jpg' file, and what is its alleged provenance?

The portrait shown in the 'Legendre.jpg' file is a watercolor caricature by Julien-Léopold Boilly, described as the only authenticated portrait of Legendre. It is based on an anonymous and undated sketch that was allegedly given by Legendre to François Arago in 1829, according to Arago's son.

Adrien-marie Legendre Wiki: Legendre's Legacy: Architect of Modern Mathematics

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Life and Career

Birth and Demise

Adrien-Marie Legendre was born in Paris, France, on September 18, 1752. He passed away in Paris on January 9, 1833, at the age of 80, following a prolonged illness.

Education and Early Career

He received his foundational education at the Collège Mazarin in Paris, successfully defending his thesis in physics and mathematics in 1770. Legendre later served as an instructor at the École Militaire in Paris from 1775 to 1780 and subsequently at the École Normale from 1795. He was also affiliated with the Bureau des Longitudes.

Recognition and Affiliations

Legendre's significant work earned him accolades, including a prize from the Berlin Academy in 1782 for his treatise on projectiles. He was appointed an adjoint member of the Académie des sciences in 1783 and an associate in 1785. In 1789, he was elected a Fellow of the Royal Society. His name is also inscribed among the 72 prominent scientists honored on the Eiffel Tower.

Revolution and Public Service

The French Revolution significantly impacted Legendre, leading to the loss of his personal fortune in 1793. Despite these challenges, he continued his academic contributions, serving as a mathematics examiner for graduating artillery students at the École Militaire and for the École Polytechnique. His pension was discontinued in 1824 due to his refusal to support a government candidate at the Institut National, though he was later made an officer of the Légion d'Honneur in 1831.

Mathematical Contributions

Calculus and Analysis

Legendre made substantial contributions to calculus and analysis. He is renowned for introducing the Legendre polynomials, which are solutions to Legendre's differential equation and frequently appear in physics and engineering, particularly in electrostatics. His work on elliptic integrals was foundational, though later completed by Abel and Jacobi. He also developed the Legendre transformation, a key tool in classical mechanics for transitioning between Lagrangian and Hamiltonian formulations, and in thermodynamics for deriving thermodynamic potentials like enthalpy and Gibbs free energy.

Number Theory

In number theory, Legendre conjectured the quadratic reciprocity law, later proven by Gauss, and introduced the Legendre symbol. He pioneered the application of analysis to number theory and made early conjectures about the distribution of prime numbers, notably the prime number theorem, which was rigorously proven by Hadamard and de la Vallée Poussin. He also provided a proof for Fermat's Last Theorem for the exponent n=5.

Statistics and Computation

Legendre is credited with first publishing the method of least squares in 1806, a technique crucial for linear regression, signal processing, and curve fitting, although Carl Friedrich Gauss had independently discovered it earlier. His work on elliptic integrals also led to the development of the Gauss-Legendre algorithm, an efficient method for approximating pi.

Foundational Texts

His influential textbook, Éléments de géométrie (1794), significantly reorganized and simplified Euclid's propositions, serving as a leading elementary geometry text for a century. His three-volume work, Exercices de Calcul Intégral (1811, 1817, 1819), further explored integral calculus, beta functions, and gamma functions, introducing notation like $\Gamma(n+1) = n!$.

Distinctions and Commemorations

Academic and Scientific Honors

Legendre was recognized globally for his intellectual achievements. He was elected a Foreign Honorary Member of the American Academy of Arts and Sciences in 1832. His enduring legacy is further cemented by celestial and terrestrial commemorations.

Celestial and Terrestrial Recognition

The crater Legendre on the Moon and the main-belt asteroid 26950 Legendre bear his name, honoring his contributions to science. A street in Paris' 17th Arrondissement is also named in his memory, reflecting his significant impact on French intellectual life.

Key Publications

Major Works

Legendre authored several seminal works that shaped mathematical thought:

Éléments de géométrie (1794) - A highly influential geometry textbook.
Essai sur la Théorie des Nombres (1797-8) - A foundational text in number theory.
Nouvelles Méthodes pour la Détermination des Orbites des Comètes (1805) - Detailing methods for celestial mechanics.
Exercices de Calcul Intégral (1811, 1817, 1819) - A comprehensive exploration of integral calculus.
Traité des Fonctions Elliptiques (1825, 1826, 1830) - A detailed study of elliptic functions.

Additionally, Legendre published numerous memoirs in prestigious scientific journals, including works on the attraction of spheroids, indeterminate analysis, and the theory of parallels.

Recherches sur la trajectoire des projectiles (1782)
Memoirs in Histoire de l'Académie Royale des Sciences (e.g., on Legendre polynomials, number theory, integration of partial differential equations).
Memoirs in Mémories présentés par divers Savants (e.g., on least squares, attraction of ellipsoids, Fermat's theorem).

The Portrait Conundrum

A Case of Mistaken Identity

For approximately two centuries, a widely circulated portrait mistakenly identified as Adrien-Marie Legendre actually depicted the French politician Louis Legendre. This error, originating from a simple label "Legendre" on an anonymous sketch, persisted until its correction in 2005. The only authenticated portraits of the mathematician are found in caricatures by Julien-Léopold Boilly, created around 1820.

References

Source Citations

Aldrich, John. Earliest Uses of Symbols of Calculus.
Duren, Peter. Changing Faces: The Mistaken Portrait of Legendre. Notices of the AMS.
Random House Webster's Unabridged Dictionary. Legendre.
Plackett, R.L. The discovery of the method of least squares. Biometrika.
Stigler, Stephen M. Gauss and the Invention of Least Squares. The Annals of Statistics.
O'Connor, John J.; Robertson, Edmund F. Adrien-Marie Legendre. MacTutor History of Mathematics Archive.
Royal Society. Library and Archive.
Weil, André. Number Theory: An approach through history From Hammurapi to Legendre.
Stigler, Stephen M. Gauss and the Invention of Least Squares. Ann. Stat.
Agarwal, Ravi P.; Sen, Syamal K. Creators of mathematical and computational sciences.
American Academy of Arts and Sciences. Book of Members, 1780–2010: Chapter L.
Review of Elements of Geometry. The North American Review.
Boilly, Julien-Léopold. Album de 73 portraits-charge aquarellés des membres de I'Institut.
Nuttle, William. Mathematics of Choice — Adrien-Marie Legendre. Eiffel’s Paris — an Engineer’s Guide.

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References

AndrÃ© Weil, Number Theory: An approach through history From Hammurapi to Legendre, Springer Science & Business Media2006, p. 325.

A full list of references for this article are available at the Adrien-Marie Legendre Wikipedia page

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Legendre's Legacy

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Life and Career 📜

📍 Birth and Demise

🎓 Education and Early Career

🌟 Recognition and Affiliations

🏛️ Revolution and Public Service

Mathematical Contributions 📈

📐 Calculus and Analysis

🔢 Number Theory

📊 Statistics and Computation

📚 Foundational Texts

Distinctions and Commemorations 🌟

🏅 Academic and Scientific Honors

🔭 Celestial and Terrestrial Recognition

Key Publications 📚

📖 Major Works

The Portrait Conundrum 👤

❓ A Case of Mistaken Identity

References 🔗

📜 Source Citations

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📜 Important Notice

Dive in with Flashcard Learning!

Life and Career

Birth and Demise

Education and Early Career

Recognition and Affiliations

Revolution and Public Service

Mathematical Contributions

Calculus and Analysis

Number Theory

Statistics and Computation

Foundational Texts

Distinctions and Commemorations

Academic and Scientific Honors

Celestial and Terrestrial Recognition

Key Publications

Major Works

The Portrait Conundrum

A Case of Mistaken Identity

References

Source Citations

Teacher's Corner

True or False?

Test Your Knowledge!

Gamer's Corner

Discover other topics to study!

References

Feedback & Support

Disclaimer

Important Notice