  Consider the rectangular triangle with sides with length 1 and 1, then the
oblique side has length square root of 2. Now construct on top of the oblique
side, a new rectangular triangle with the oblique side as rectangle side and a
second rectangle side of length 1. Continue this process indefinitely, what you
get is called "the spiral of Theodorus". Now the question is: Can there be two
hypothenusa (oblique sides) which lie on the same line? Apparently there can't.
A proof of this proposition was given in 1958, but to our knowledge no other
proofs are available. Since we had no access to the journal, we wanted to prove
it again.
