# Definition:Calculus of Variations/Historical Note

## Historical Note on Calculus of Variations

Some sources suggest that, in a sense, the earliest problem in the calculus of variations arose in one of the legends of the founding of Carthage; the city was granted as much land as could be enclosed by a given length.

The calculus of variations emerged as a branch of mathematics as a result of investigations into the cycloid in the $18$th century.

The first systematic investigation of the topic was given by Joseph Louis Lagrange in his earliest and most important works, together with Leonhard Paul Euler, who coined the term in $1766$.

Karl Weierstrass ushered in a new era of precise reasoning with his lectures in $1879$ on the subject. One of his students, Oskar Bolza, took on the subject and developed the Chicago school of the calculus of variations.

## Sources

- 1937: Eric Temple Bell:
*Men of Mathematics*... (previous) ... (next): Chapter $\text{VIII}$: Nature or Nurture? - 1972: George F. Simmons:
*Differential Equations*... (previous) ... (next): $\S 3$: Appendix $\text A$: Euler - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {A}.15$: Torricelli ($1608$ – $1647$) - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {A}.21$: Euler ($1707$ – $1783$) - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {A}.22$: Lagrange ($1736$ – $1813$) - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {A}.33$: Weierstrass ($1815$ – $1897$)