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i´d like to plot a interpretation of a map that transforms the interval [0,1] to the unit circle.

And also the same with a rectangle that is transformed to a cylinder which then is transformed into the torus.

Unfortunately i have no idea how to implement this picture.

Can someone show me how to do it please ? I added a picture because it is difficult to explain exactly what i needenter image description here.

McBotto.t
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