There are already several versions of a geometric proof by infinite descent so maybe another isn't needed. BUT I did not see this version( maybe I overlooked it...) which is especially visually clear to people who are less scared by rectangles than by triangles (I'll describe rather than draw the diagram): Take a rectangle in proportions 1 to sqrt(2) (like an ideal sheet of A4 paper). Remove a largest square from the top leaving one with proportions 1 to sqrt(2)-1 along the base. Then remove a largest possible square from the right side of this smaller rectangle. The result is an even smaller rectangle proportional to the first. SO (as usual) the Euclidean algorithm never ceases.

Thank you. It is certainly worth mentioning.

What is your name? I'd like to give a credit.

Aaron Meyerowitz meyerowi@fau.edu

I suppose the smaller rectangle is rotated 90 degrees. Here is a link to a kind of hokey book The Elements of Dynamic Symmetry By Jay Hambidge which has a picture.

http://books.google.com/books?id=F4C6YelrRrEC&printsec=frontcover&dq=jay+hambidge&ei=bEqfSbnqGoLeyASrg5GMAg#PPA43,M1

Very good. Thank you.