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: https://www.youtube.com/playlist?list=PLw3pvR_YJeRcMaubDZvkjayqDJT4Tx47A 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: https://www.youtube.com/channel/UCYLOc-m8WuQaBHJ56lEw4VQ