For a pythagorean triple a2 + b2 = c2, can the L's from an a x a square and a b x b square can be packed into a c x c square? The following pictures show that this is sometimes possible. There are 3 infinite families of packings illustrated below.
32 + 42 = 52 | ![]() |
52 + 122 = 132 | ![]() |
72 + 242 = 252 | ![]() |
42 + 32 = 52 | ![]() |
82 + 152 = 172 | ![]() |
122 + 352 = 372 | ![]() |
122 + 52 = 132 | ![]() |
282 + 452 = 532 | ![]() |