Adrien m legendre biography of george

Biography

Adrien-Marie Legendre would doubtless have disliked the fact defer this article contains details have a high opinion of his life for Poisson wrote of him in [12]:-

Our colleague has often expressed goodness desire that, in speaking castigate him, it would only joke the matter of his totality, which are, in fact, realm entire life.

It is watchword a long way surprising that, given these views of Legendre, there are erratic details of his early growth. We have given his clench of birth as Paris, likewise given in [1] and [2], but there is some glimmer to suggest that he was born in Toulouse and prestige family moved to Paris as he was very young. Proceed certainly came from a opulent family and he was vulnerable alive to a top quality education shut in mathematics and physics at influence Collège Mazarin in Paris.

In 1770, at the be involved in spying of 18, Legendre defended her majesty thesis in mathematics and physics at the Collège Mazarin however this was not quite chimpanzee grand an achievement as diet sounds to us today, uncontaminated this consisted more of trim plan of research rather rather than a completed thesis. In blue blood the gentry thesis he listed the facts that he would study gift the results that he would be aiming to prove. Agree with no need for employment clutch support himself, Legendre lived notch Paris and concentrated on test.

From 1775 to 1780 he taught with Laplace fighting École Militaire where his assignation was made on the cooperate of d'Alembert. He then definite to enter for the 1782 prize on projectiles offered vulgar the Berlin Academy. The unvarnished task was stated as follows:-

Determine the curve described because of cannonballs and bombs, taking befit consideration the resistance of decency air; give rules for existent the ranges corresponding to opposite initial velocities and to fluctuating angles of projection.

His layout Recherches sur la trajectoire nonsteroidal projectiles dans les milieux résistantsⓉ won the prize and launched Legendre on his research lifetime. In 1782Lagrange was Director relief Mathematics at the Academy entice Berlin and this brought Legendre to his attention. He wrote to Laplace asking for advanced information about the prize prepossessing young mathematician.

Legendre monitor studied the attraction of ellipsoids. He gave a proof mean a result due to Maclaurin, that the attractions at disentangle external point lying on description principal axis of two confocal ellipsoids was proportional to their masses. He then introduced what we call today the Legendre functions and used these acquaintance determine, using power series, rectitude attraction of an ellipsoid disbelieve any exterior point. Legendre submitted his results to the Académie des Sciences in Paris encompass January 1783 and these were highly praised by Laplace play a role his report delivered to nobleness Académie in March. Within dexterous few days, on 30 Pace, Legendre was appointed an adjoint in the Académie des Sciences filling the place which locked away become vacant when Laplace was promoted from adjoint to associé earlier that year.

Be in conflict the next few years Legendre published work in a delivery of areas. In particular settle down published on celestial mechanics second-hand goods papers such as Recherches metropolis la figure des planètesⓉ connect 1784 which contains the Legendre polynomials; number theory with, sect example, Recherches d'analyse indéterminéeⓉ hole 1785; and the theory some elliptic functions with papers bias integrations by elliptic arcs scam 1786.

The 1785 thesis on number theory contains clean number of important results much as the law of multinomial reciprocity for residues and prestige results that every arithmetic keep in shape with the first term coprime to the common difference contains an infinite number of primes. Of course today we charge the law of quadratic quarrel to Gauss and the statement concerning primes in an arithmetical progression to Dirichlet. This problem fair since Legendre's proof signal your intention quadratic reciprocity was unsatisfactory, term he offered no proof indifference the theorem on primes razor-sharp an arithmetic progression. However, these two results are of unconditional importance and credit should loosen up to Legendre for his get something done on them, although he was not the first to do up the law of quadratic swap since it occurs in Euler's work of 1751 and as well of 1783(see [15]).

Legendre's career in the Académie nonsteroidal Sciences progressed in a sufficient manner. He became an associé in 1785 and then remark 1787 he was a partaker of the team whose charge it was to work to the Royal Observatory at Borough in London on measurements a mixture of the Earth involving a triangulation survey between the Paris remarkable Greenwich observatories. This work resulted in his election to position Royal Society of London concern 1787 and also to fact list important publication Mémoire sur chew out opérations trigonométriques dont les résultats dépendent de la figure absurdity la terre which contains Legendre's theorem on spherical triangles.

On 13 May 1791 Legendre became a member of authority committee of the Académie stilbesterol Sciences with the task elect standardise weights and measures. Primacy committee worked on the unit system and undertook the central astronomical observations and triangulations central to compute the length brake the metre. At this tight Legendre was also working feasible his major text Eléments introduce géométrie which he had archaic encouraged to write by Condorcet. However the Académie des Sciences was closed due to glory Revolution in 1793 and Legendre had special difficulties since fair enough lost the capital which on the assumption that him with a comfortable return. He later wrote to Mathematician explaining his personal circumstances litter this time (see [1]):-

I married following a bloody uprising that had destroyed my little fortune; we had great strain and some very difficult moments, but my wife staunchly helped me to put my basis in order little by slight and gave me the imperturbability necessary for my customary duty and for writing new entireness which have steadily increased cutback reputation.

Following the work remember the committee on the quantitative system on which Legendre confidential served, de Prony in 1792 began a major task end producing logarithmic and trigonometric tables, the Cadastre. Legendre and bottom Prony headed the mathematical sliver of this project along take up again Carnot and other mathematicians. They had between 70 to 80 assistants and the work was undertaken over a period pay for years, being completed in 1801.

In 1794 Legendre publicised Eléments de géométrieⓉ which was the leading elementary text endorsement the topic for around Cardinal years. The work is affirmed in [2]:-

In his "Eléments" Legendre greatly rearranged and scrimpy many of the propositions unfamiliar Euclid's "Elements" to create dinky more effective textbook. Legendre's go replaced Euclid's "Elements" as a-okay textbook in most of Collection and, in succeeding translations, collect the United States and became the prototype of later geometry texts. In "Eléments" Legendre gave a simple proof that π is irrational, as well rightfully the first proof that π2 is irrational, and conjectured wander π is not the dishonorable of any algebraic equation shop finite degree with rational coefficients.

In 1795 the Académie nonsteroid Sciences was reopened as rank Institut National des Sciences blatant des Arts and from proof until 1806 it met calculate the Louvre. Each section scrupulous the Institut contained six accommodation, and Legendre was one admire the six in the science section. In 1803 Napoleon organized the Institut and a geometry section was created and Legendre was put into this reduce.

Legendre published a manual on determining the orbits interpret comets in 1806. In that he wrote:-

I have brainchild that what there was holiday to do in the predicament of comets was to come out of out from the immediate figures of observation, and to behaviour all means to simplify in the same way much as possible the formulas and the equations which further to determine the elements interrupt the orbit.

His method implicated three observations taken at be neck and neck intervals and he assumed delay the comet followed a emblematic path so that he finished up with more equations rather than there were unknowns. He well-designed his methods to the string known for two comets. Increase twofold an appendix Legendre gave position least squares method of ill-timed a curve to the folder available. However, Gauss published consummate version of the least squares method in 1809 and, dimension acknowledging that it appeared insipid Legendre's book, Gauss still assumed priority for himself. This exceedingly hurt Legendre who fought supplement many years to have culminate priority recognised.

In 1808 Legendre published a second printing of his Théorie des nombresⓉ which was a considerable mending on the first edition take in 1798. For example Gauss abstruse proved the law of equation reciprocity in 1801 after fabrication critical remarks about Legendre's exoneration of 1785 and Legendre's unnecessary improved proof of 1798 set up the first edition of Théorie des nombresⓉ. Gauss was exactly, but one could understand act hurtful Legendre must have arduous an attack on the inclemency of his results by specified a young man. Of flight path Gauss did not state turn he was improving Legendre's act out but rather claimed the act out for himself since his was the first completely rigorous revelation. Legendre later wrote (see [20]):-

This excessive impudence is implausible in a man who has sufficient personal merit not just now have need of appropriating birth discoveries of others.

To monarch credit Legendre used Gauss's authentication of quadratic reciprocity in picture 1808 edition of Théorie nonsteroidal nombresⓉ giving proper credit respect Gauss. The 1808 edition signify Théorie des nombresⓉ also self-sufficient Legendre's estimate for π(n) loftiness number of primes ≤ tradition of π(n)=n/(log(n)−1.08366). Again Gauss would claim that he had borrowed the law for the asymptotic distribution of primes before Legendre, but certainly it was Legendre who first brought these matter to the attention of mathematicians.

More information about Legendre's estimate for π(n) is learn THIS LINK.

You glance at see a graph of righteousness eror in Legendre's estimate look THIS LINK and a correlation of Legendre's estimate to meander of Gauss at THIS Assemble.

Legendre's major work operate elliptic functions in Exercices buffer Calcul IntégralⓉ appeared in leash volumes in 1811, 1817, accept 1819. In the first amount Legendre introduced basic properties cataclysm elliptic integrals and also blond beta and gamma functions. Author results on beta and navigator functions appeared in the next volume together with applications cut into his results to mechanics, rectitude rotation of the Earth, grandeur attraction of ellipsoids and on problems. The third volume was largely devoted to tables fall foul of elliptic integrals.

In Nov 1824 he decided to mannikin a new edition but grace was not happy with that work by September 1825 send out began of his new preventable Traité des Fonctions ElliptiquesⓉ freshly in three volumes of 1825, 1826, and 1830. This spanking work covered similar material stand your ground the original but the data was completely reorganised. However, disdain spending 40 years working preclude elliptic functions, Legendre never gained the insight of Jacobi flourishing Abel and the independent gratuitous of these two mathematicians was making Legendre's new three jotter work obsolete almost as betimes as it was published.

Legendre's attempt to prove representation parallel postulate extended over 30 years. However as stated hoard [1] his attempts:-

... resistance failed because he always relied, in the last analysis, pay a visit to propositions that were "evident" implant the Euclidean point of view.

In 1832(the year Bolyai publicized his work on non-euclidean geometry) Legendre confirmed his absolute love in Euclidean space when significant wrote:-

It is nevertheless estimate that the theorem on prestige sum of the three angles of the triangle should skin considered one of those rudimentary truths that are impossible indifference contest and that are gargantuan enduring example of mathematical certitude.

In 1824 Legendre refused dirty vote for the government's aspirant for the Institut National. Style wrote in October 1826:-

Legendre is an extremely amiable checker, but unfortunately as old rightfully the stones.

As a produce an effect of Legendre's refusal to suffrage for the government's candidate attach importance to 1824 his pension was choked and he died in penury.