Editing Pythagorean triple (section)

==Examples==

<!--Please DO NOT add any triples of the form ka, kb, kc where a, b, and c are integers and k > 1. Please note the definition of a primitive Pythagorean triple, one in which the terms are relatively prime.-->

[[File:Pythagorean Triples Scatter Plot.png|thumb|[[Scatter plot]] of the legs ({{math|''a''}}, {{math|''b''}}) of the first Pythagorean triples with {{math|''a''}} and {{math|''b''}} less than 6000. Negative values are included to illustrate the parabolic patterns. The "rays" are a result of the fact that if {{math|(''a'', ''b'', ''c'')}} is a Pythagorean triple, then so is {{math|(2''a'', 2''b'', 2''c'')}}, {{math|(3''a'', 3''b'', 3''c'')}} and, more generally, {{math|(''ka'', ''kb'', ''kc'')}} for any positive integer {{math|''k''}}.]]

There are 16 primitive Pythagorean triples of numbers up to 100:
{| style="margin:auto;"  cellspacing="0" cellpadding="0"
|- style="text-align:right;"
|style="padding:0 1em"| (3, 4, 5)
|style="padding:0 1em"| (5, 12, 13)
|style="padding:0 1em"| (8, 15, 17)
|style="padding:0 1em"| (7, 24, 25)
|- style="text-align:right;"
|style="padding:0 1em"| (20, 21, 29)
|style="padding:0 1em"| (12, 35, 37)
|style="padding:0 1em"| (9, 40, 41)
|style="padding:0 1em"| (28, 45, 53)
|- style="text-align:right;"
|style="padding:0 1em"| (11, 60, 61)
|style="padding:0 1em"| (16, 63, 65)
|style="padding:0 1em"| (33, 56, 65)
|style="padding:0 1em"| (48, 55, 73)
|- style="text-align:right;"
|style="padding:0 1em"| (13, 84, 85)
|style="padding:0 1em"| (36, 77, 85)
|style="padding:0 1em"| (39, 80, 89)
|style="padding:0 1em"| (65, 72, 97)
|}
Other small Pythagorean triples such as (6, 8, 10) are not listed because they are not primitive; for instance (6, 8, 10) is a multiple of (3, 4, 5).

Each of these points (with their multiples) forms a radiating line in the scatter plot to the right.

Additionally, these are the remaining primitive Pythagorean triples of numbers up to 300:
{| style="margin:auto;"  cellspacing="0" cellpadding="0"
|- style="text-align:right;"
|style="padding:0 1em"| (20, 99, 101)
|style="padding:0 1em"| (60, 91, 109)
|style="padding:0 1em"| (15, 112, 113)
|style="padding:0 1em"| (44, 117, 125)
|- style="text-align:right;"
|style="padding:0 1em"| (88, 105, 137)
|style="padding:0 1em"| (17, 144, 145)
|style="padding:0 1em"| (24, 143, 145)
|style="padding:0 1em"| (51, 140, 149)
|- style="text-align:right;"
|style="padding:0 1em"| (85, 132, 157)
|style="padding:0 1em"| (119, 120, 169)
|style="padding:0 1em"| (52, 165, 173)
|style="padding:0 1em"| (19, 180, 181)
|- style="text-align:right;"
|style="padding:0 1em"| (57, 176, 185)
|style="padding:0 1em"| (104, 153, 185)
|style="padding:0 1em"| (95, 168, 193)
|style="padding:0 1em"| (28, 195, 197)
|- style="text-align:right;"
|style="padding:0 1em"| (84, 187, 205)
|style="padding:0 1em"| (133, 156, 205)
|style="padding:0 1em"| (21, 220, 221)
|style="padding:0 1em"| (140, 171, 221)
|- style="text-align:right;"
|style="padding:0 1em"| (60, 221, 229)
|style="padding:0 1em"| (105, 208, 233)
|style="padding:0 1em"| (120, 209, 241)
|style="padding:0 1em"| (32, 255, 257)
|- style="text-align:right;"
|style="padding:0 1em"| (23, 264, 265)
|style="padding:0 1em"| (96, 247, 265)
|style="padding:0 1em"| (69, 260, 269)
|style="padding:0 1em"| (115, 252, 277)
|- style="text-align:right;"
|style="padding:0 1em"| (160, 231, 281)
|style="padding:0 1em"| (161, 240, 289)
|style="padding:0 1em"| (68, 285, 293)
|}