A video inspired by the mathematician, Steve Strogatz. At the age of thirteen, Steve was astonished to find that pendulums and water fountains had a strange relationship that had previously been completely hidden from him.
Parabolas (etc.) from Radiolab, which has us running around looking for parabolas everywhere we go. A few comments for the video point out that many of the shapes in the video are not parabolas—”a plane curve which is mirror-symmetrical and is approximately U-shaped”—but are actually catenaries—”the curve that an idealized hanging chain or cable assumes under its own weight when supported only at its ends. The catenary curve has a U-like shape, superficially similar in appearance to a parabolic arch, but it is not a parabola.”
Related exploration: Catenary vs Parabola.
Updated video and links.