Here's a beautiful short film demonstrating mathematical principles as they appear in nature: Nature by Numbers. In the video, illustrator CristÃ³bal Vila demonstrates how the Fibonacci Sequence is visible in a Nautilus shell, and proceeds through the Golden Ratio, Golden Angle, Voronoi Tessellations, and the Delaunay Condition. (Yeah, I hadn't heard of those last two either.) For more details about the math behind this film, and how the Nautilus example is actually a bit flubbed, read Vila's explanation of the film (in both English and Spanish).
Recommended for: people who like neat animation, easy-to-understand math, and/or something to divert them on a day when not much else is happening online.