关于悬链线的一点注记(英文)

A Note on Catenary

悬链线是微积分、微分方程、微分几何、变分计算及数值分析中的一个重要课题。本文通过一些诸如方轮自行车、旋转的最小面积等有趣的例子,计算悬链线和相应半圆下面的面积,证明悬链线到处都有,但并不是无处不在。

Catenary is an important topic in calculus, differential equations, differential geometry, variational calculus, and even in numerical analysis. A great deal of work has been reported regarding the catenary. In this note, in addition to some interesting examples of the catenary in geometry such as the square wheels bicycle, minimal surface of revolution, by calculating the areas below the catenary and half - circle, we show, even in geometry, the catenary is not everywhere.