Even better picture (and explanation) in this paper: Faessler, Albert. "Multiple Pythagorean Number Triples". IMA Preprint Series #438, August 1988. Referenced by Wikipedia article on Pythagorean Triples. Very nice & pertinent discussion of the distribution of Pythagorean triples. From: http://conservancy.umn.edu/bitstream/4878/1/438.pdf Size: 484 KB (495,306 bytes) At 11:37 PM 8/15/2013, Dan Asimov wrote:
That's a beautiful and intriguing map of the Moon that Fred posted. Those areas of avoidance almost look like parts of a Petri dish where antibiotics keep a mold from growing. It looks as if it would take a lot of mathematical explaining to understands why it looks that way.
A much less interesting pattern, but interesting nonetheless, is this Wikipedia plot of all Pythagorean legs (a,b) of a triple a^2 + b^2 = c^2 for all |a|, |b| <= 6000:
< http://upload.wikimedia.org/wikipedia/commons/9/97/Pythagorean_triple_scatte... >.