These patterns can be explained as follows. If formula_76 is an integer, then ("a", formula_77, formula_78) is a Pythagorean triple. (In fact every Pythagorean triple ("a", "b", "c") can be written in this way with integer "n", possibly after exchanging "a" and "b", since formula_79 and "a" and "b" cannot both be odd.) The Pythagorean triples thus lie on curves given by formula_80, that is, parabolas reflected at the "a"-axis, and the corresponding curves with "a" and "b" interchanged. If "a" is varied for a given "n" (i.e. on a given parabola), integer values of "b" occur relatively frequently if "n" is a square or a small multiple of a square. If several such values happen to lie close together, the corresponding parabolas approximately coincide, and the triples cluster in a narrow parabolic strip. For instance, 382 = 1444, 2 × 272 = 1458,