The Catenary (hanging chain), how it was first solved.

The catenary is the mathematical shape of a hanging chain. Describing this shape is one of the famous original problems of calculus. I discuss the history of the problem, how it was determined that the curve was not a parabola, how to model the curve with a differential equation based on the balance of forces, and how the equation was first solved by Bernoulli, Leibniz, and Huygens. Bernoulli's solution involves the solution of another problem: the rectification of a parabola, or finding it's arc-length. This lecture illustrates most of the ideas in a second semester of Calculus. This video is Episode 8 in a series I call Tricky Parts of Calculus, a series that covers the subtle and difficult topics in calculus that are usually missed in a calculus class. See the whole playlist here:    • Tricky Parts of Calculus   Also check out my channel for general advice and opinions about math, as well as the Daniel Rubin Show podcast for interesting conversations about math and other topics:    / @danielrubin1