Joseph Louis Lagrange

As long as algebra and geometry have been separated, their progress have been slow and their uses limited; but when these two sciences have been united, they have lent each mutual forces, and have marched together towards perfection.

Joseph Louis Lagrange was born 1736 in Turin, Italy. Because of his French ancestors, many considered him the Italian born French mathematician. In 1787 he became a member of the French Academy and remained in France until his death in 1813. Although his father wanted him to be a lawyer, Lagrange became interested in mathematics after reading a copy of Halley's work on the use of algebra in optics in 1693. When he was 16 years old, he began studying mathematics on his own and by the time he hit 19, he was appointed to professorship at the Royal Artillery School in Turin. Napoleon named him the Legion of Honour and made him Count of the Empire in 1808.

Lagrange accomplished several things in his lifetime. When he was twenty years old he sent a solution that he had discovered for deriving the central equation in the calculus of variations to Euler, therefore becoming one of the creators. He had a part in extending the method of solving differential equations and applied differential calculus to the theory of probabilities. He also proved that every natural number is a sum of squares. For example, 10 = 1 + 1 + 4 + 4 and 30 = 1 + 4 + 9 + 16. These solutions and the way Lagrange applied them to mechanics were so great that he was regarded by many the greatest living mathematician by the age of 25.

Lagrange became the first professor of analysis at the Ecole Polytechnique in 1974. Lagrange based many of his lectures on the differential calculus on Theorie des fonctions analytiques which was published in 1797. This work was an extended version of an idea he had had which he sent to Berlin in 1772. The object was to substitute for the differential calculus a group of theorems based on the development of algebraic functions. The book was divided into three parts; the first discusses the general theory of functions, the second deals with applications to geometry and the third with applications to mechanics. These works devoted to differential calculus and variations can be considered the starting point for the Cauchy, Jacobi and Weierstrass.

He composed several papers but one of his greatest was the Mechanique analytique. In this piece of work he laid down the law of virtual work and from this principle deduced the whole of mechanics of solids and fluids. The idea behind his book was to give a general formula from which any result could be found. The following is the formula that he came up with.

(1)
\begin{align} \frac{d}{dt} \frac{\partial T}{\partial \dot{\theta}} -{\partial T}{\partial \theta} + \frac{\partial V}{\partial \theta} = 0 \end{align}

Work Cited

Rouse Ball, W.W Joseph Louis Lagrange (1736 – 1813). Retrieved March 17, 2008, Web site: http://www.maths.tcd.ie/pub/HistMath/People/Lagrange/RouseBall/RB_Lagrange.html

Joseph Louis Lagrange. Retrieved March 17, 2008, Web site: http://en.wikipedia.org/wiki/Joseph_Louis_Lagrange#Lagrangian_mechanics

Peterson, Ivars. "All square: a surprising, far-reaching overhaul for theories about quadratic expressions." Science News 169.10 (March 11, 2006): 152(2). Academic OneFile. Gale. Thames Valley DSB. 17 Mar. 2008
http://find.galegroup.com/ips/start.do?prodId=IPS

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