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Questions tagged [lagrange]

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Did Lagrange ever made mathematical mistakes in the books or papers he published? [closed]

What's interesting about Lagrange to me is that all the descriptions of him by his contemporaries, and even a century later, essentially make him seem perfect. has he ever made any mathematical ...
olipo's user avatar
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-2 votes
1 answer
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Does Lagrange's FTA proof meet rigorous requirements even by modern standards?

I know that Gauss pointed out flaws in Euler and d'Alembert's FTA proof when he submitted the FTA proof as a doctoral thesis in 1799, but I don't think I've ever seen any mention of Lagrange, so I'm ...
Lag's user avatar
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3 votes
1 answer
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Where did Lagrange prove the Four Squares Theorem?

I am trying to confirm the initial publication of Lagrange's Four Squares Theorem. Most of my sources give that it was proved by him in $1770$. However, the generally very good Penguin Dictionary of ...
Prime Mover's user avatar
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7 votes
1 answer
1k views

How does Legendre transformation in classical mechanics relate to Adrien-Marie Legendre?

I tried to look for the history of Legendre transformation, which transformed Lagrangian mechanics to Hamiltonian mechanics, usually formulated as $$ \begin{cases} p_i = \frac{\partial L}{\partial v_i}...
Mr. Egg's user avatar
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2 votes
1 answer
250 views

Where did Lagrange write his technique of resolvents for solving polynomials?

From Andrew Ellinor & Satyajit Mohanty's article on a technique for solving cubics: Using Lagrange's resolvents, to solve the cubic, one has to first solve a quadratic. Given the general cubic, $$...
Hisham's user avatar
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0 votes
0 answers
78 views

How did Newton, Lagrange, Hamilton and others ideate their mechanical formulations?

What exactly did Lagrange do, historically? This is very relevant but the accepted answer just does similar speculations based on contextual details that I have done. It was mentioned that part of ...
Hisham's user avatar
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1 vote
1 answer
165 views

Book suggestions on Lagrangian and Hamiltonian mechanics?

What are some books that talk about the origins of Lagrangian and Hamiltonian mechanics? I would like to dig deeper into the fundamental approach and the fundamentals of action and its principles.
Muneer Ahamad Shaik's user avatar
4 votes
0 answers
129 views

Lagrange's Theorem as he stated it

In Wikipedia, I found that Lagrange did not state Lagrange's Theorem in its general form. He stated "If a Polynomial in $n$ variables has its variables permuted in all $n!$ ways, the number of ...
Saikat's user avatar
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3 votes
0 answers
114 views

How did Ruffini manage to extend the methods of Lagrange in order to "prove" the insolvability of the general quintic equation?

Since Lagrange published his Reflections papers during the early 1770s — around 30 years before Ruffini took up and extended the subject — I was wondering if there were any results that were ...
GEP's user avatar
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0 votes
0 answers
86 views

Was Lagrange the first to have used generalized coordinates?

I was wondering if Lagrange was the first to use generalized coordinates as defined by their wikipedia article.
GEP's user avatar
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0 votes
1 answer
92 views

What are the direct predecessors of Lagrange's theory of quadratic forms?

I was reading Stillwell's Mathematics and its History, where Lagrange's theory of quadratic forms is synoptically presented, and I was wondering of what are the direct predecessors of the theory. ...
GEP's user avatar
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2 votes
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Where can I find Lagrange’s original equilateral triangular solution for arbitrary masses?

This answer to What kind of triangle is formed by three unequal masses in a circular restricted three body orbit? explains that In the Newtonian limit, an equilateral 3-body solution exists for any ...
uhoh's user avatar
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0 votes
2 answers
741 views

Does the word "God" appear regularly in the works of Joseph Lagrange?

In the Religious opinions section of the Wikipedia article on Laplace, there is an excerpt from Antommarchi's "The Last Moments of Napoleon", in which it is written that the name of God appeared ...
GEP's user avatar
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0 votes
1 answer
72 views

What was Lagrange's contribution to the Knights Tour Problem?

Did Lagrange make any noteworthy contribution to the Knights Tour Problem?
GEP's user avatar
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0 votes
1 answer
157 views

Was Lagrange aware of Hamiltonian mechanics?

In the book "The Road to Reality", Penrose claims that Joseph Lagrange was aware of Hamiltonian mechanics. Is there any evidence that this statement is true?
GEP's user avatar
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8 votes
0 answers
312 views

What exactly was Lagrange's "grave mistake" with respect to rotating bodies under hydrostatic equilibrium?

A comment below What would be different about satellite orbits if Earth were prolate? Would we have Sun-synchronous and Molniya orbits? got me reading Wikipedia's Jacobi ellipsoid which begins: ...
uhoh's user avatar
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26 votes
1 answer
4k views

How was Lagrange appointed professor of mathematics so early?

It is well-known that in 1755 Lagrange was appointed Professor of Mathematics at the Royal Artillery School in Turin. He was 19. His work up until then involves correspondence with Euler. Was he ...
Rain's user avatar
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2 votes
0 answers
266 views

Why did Lagrange say that Cauchy should learn literature before mathematics?

From Bruno Belhoste's Augustin-Louis Cauchy — A Biography: Even if we should doubt the remark Valson attributed to Lagrange, it is likely that he did advise Louis-François about to his son's ...
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