I read came across Fermats Libraries scan of the Zhoubi suanjing
http://fermatslibrary.com/s/pythagorean ... i-suanjing
Being an eulerian I could not help but noticing the pythagorean triples on the second sheet - (3,4,5) and (7,24,25). I was able to show that such a construction will produce triples for every odd sided square.
Can't help but wonder if there is such a construction in the first square. What do you guys think?