Editing Euler–Lagrange equation (section)

==History==
[[File:Tautochrone curve.gif|thumb|The Euler–Lagrange equation was developed in connection with their studies of the [[tautochrone]] problem. ]]
The Euler–Lagrange equation was developed in the 1750s by Euler and Lagrange in connection with their studies of the [[tautochrone]] problem. This is the problem of determining a curve on which a weighted particle will fall to a fixed point in a fixed amount of time, independent of the starting point.

Lagrange solved this problem in 1755  and sent the solution to Euler. Both further developed Lagrange's method and applied it to [[mechanics]], which led to the formulation of [[Lagrangian mechanics]]. Their correspondence ultimately led to the [[calculus of variations]], a term coined by Euler himself in 1766.<ref>[http://numericalmethods.eng.usf.edu/anecdotes/lagrange.pdf A short biography of Lagrange] {{webarchive|url=https://web.archive.org/web/20070714022022/http://numericalmethods.eng.usf.edu/anecdotes/lagrange.pdf |date=2007-07-14 }}</ref>