mathematical origami -- follow-up from 1999 sci.math thread

In 1999, I asked a question in sci.math :

''Is it possible to continuously deform a rectangle in space isometrically in such a way that the end result (the crumpled sheet of paper) fits inside a sphere of arbitrarily small diameter? (self-intersections are not allowed. For example, folding a square into two twice with the end result a square whose sides are half the size of the original one is illegal)'

The entire thread can be read by searching the archives at google groups with entry: ''crumpling a sheet of paper isometrically'.

John Rickard answered affirmatively and described how it could be done. Later, it appeared to me that the deformation could be simplified

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Sorry about the bad link above. I hope this one will work: http://members.nbci.com/ezcos/

The scanned image is at the very top of the page.