Keywords: Torus from rectangle.gif A torus can be constructed by two transformations on a rectangle First we bend along one direction joining opposite sides creating a cylinder Then we bend the cylinder so the ends are joined The resulting figure is a torus However the second transformation does not preserve lengths on the surface as can be observed by the extension and compression of the checkered pattern Here's the diagram of this process File TorusAsSquare svg own Kieff Torus surfaces Mathematical animations Animated GIF Created with Persistence of Vision |