Three segments: A) "Volume Filling Surfaces": three dimensional analog of the Sierpinski curve in the "Space Filling Curves" video, a limit surface which fills up a cube. The viewpoint moves closer to the center of the cube as the approximating surfaces become more complicated, producing a...

This video defines the meaning of a regular curve (a smooth closed curve) in the plane, and the rules for a regular homotopy between regular curves. It then defines the rotation number of a regular curve, and proves that there is a regular homotopy between two regular curves only if they have the...

This video completes the proof of Whitney Graustein theorem, by showing that if two regular curves have the same rotation number, then there is a regularly homotopy between them. The construction of the regular homotopy proceeds by the same algorithm that was used to produce the computer...