# 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? - 1963: Charles Fox:
*An Introduction to the Calculus of Variations*(2nd ed.) ... (previous) ... (next): Chapter $\text I$. The First Variation: $1.1$. Introduction - 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 ($\text {1608}$ – $\text {1647}$) - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {A}.21$: Euler ($\text {1707}$ – $\text {1783}$) - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {A}.22$: Lagrange ($\text {1736}$ – $\text {1813}$) - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {A}.33$: Weierstrass ($\text {1815}$ – $\text {1897}$)