4||0|90|0|
0|0|0|||||Irationality of root 2|Aaron|1|15:50:01|02/20/2009|There are already several versions of a geometric proof by infinite descent so maybe another isn%27t needed. BUT I did not see this version%28 maybe I overlooked it...%29 which is especially visually clear to people who are less scared by rectangles than by triangles %28I%27ll describe rather than draw the diagram%29%3A Take a rectangle in proportions 1 to sqrt%282%29 %28like an ideal sheet of A4 paper%29. Remove a largest square from the top leaving one with proportions 1 to sqrt%282%29-1 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 %28as usual%29 the Euclidean algorithm never ceases.
2|1|0|||||RE%3A Irationality of root 2|alexb||17:02:53|02/20/2009|Thank you. It is certainly worth mentioning.%0D%0A%0D%0AWhat is your name%3F I%27d like to give a credit.
3|2|2|||||RE%3A Irationality of root 2|Aaron|1|21:58:20|02/20/2009|Aaron Meyerowitz meyerowi%40fau.edu%0D%0A%0D%0AI 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.%0D%0A%0D%0Ahttp%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DF4C6YelrRrEC%26printsec%3Dfrontcover%26dq%3Djay%2Bhambidge%26ei%3DbEqfSbnqGoLeyASrg5GMAg%23PPA43%2CM1%0D%0A%0D%0A
4|3|3|||||RE%3A Irationality of root 2|alexb||21:59:29|02/20/2009|Very good. Thank you.