All possible pythagorean triples, visualized

3,086,907 views -- May 26, 2017

https://www.youtube.com/watch?v=QJYmyhnaaek

i found this 20 min. ago....

watching these clips by 3Blue1Brown (4.59M subscribers) ...
i often wonder ... Will these clips make Martin-Gardner (like) articles obsolete (forgotten) ?

On Friday, June 24, 2022 at 11:14:52 AM UTC-7, Jonathan Dushoff wrote:
> Thanks!
>
> Doing that made me notice that I put the code together in a big hurry, and was only finding triples where c is itself a sum of squares (which excludes things like (9, 12, 15) where c is the product of a sum of square and and a non-SOS factor). The whole thing has become a bit of a rabbit hole for me, but here is a possibly pedagogical plot.
>
> http://dushoff.github.io/notebook/outputs/rp.newpyth.Rout.pdf
> On Tuesday, June 21, 2022 at 1:23:15 PM UTC-4, henh...@gmail.com wrote:
> > On Tuesday, June 21, 2022 at 9:20:25 AM UTC-7, Jonathan Dushoff wrote:
> > > If you're interested in these patterns, you might like this picture of the triples that I made a few years ago http://dushoff.github.io/notebook/pythagoras.html.
> > thanks!
> > (for pedagogical reasons) or for pedagogical purposes,
> > students would want to see a graph showing the first 5 or the first 10 plot- points.
> > > > > (load "pyth.lsp")
> > > > >
> > > > > ( 3, 4, 5 )
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> > > > > ( 5, 12, 13 )
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> > > > > ( 6, 8, 10 )
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> > > > > ( 7, 24, 25 )
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> > > > > ( 8, 15, 17 )
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> > > > > ( 9, 12, 15 )
> > > > > ( 9, 40, 41 )
> > > > >
> > > > > ( 10, 24, 26 )
> > > > >
> > > > > ( 11, 60, 61 )
> > > > >
> > > > > ( 12, 16, 20 )
> > > > > ( 12, 35, 37 )
> > > > >
> > > > > ( 13, 84, 85 )
> > > > >
> > > > > ( 14, 48, 50 )
> > > > >
> > > > > ( 15, 20, 25 )
> > > > > ( 15, 36, 39 )
> > > > > ( 15, 112, 113 )
> > > > >
> > > > > ( 16, 30, 34 )
> > > > > ( 16, 63, 65 )
> > > > >
> > > > > ( 17, 144, 145 )
> > > > >
> > > > > ( 18, 24, 30 )
> > > > > ( 18, 80, 82 )
> > > > >
> > > > > ( 19, 180, 181 )
> > > > >
> > > > > ( 20, 21, 29 )
> > > > > ( 20, 48, 52 )
> > > > > ( 20, 99, 101 )
> > > > >
> > > > > ( 21, 28, 35 )
> > > > > ( 21, 72, 75 )
> > > > > ( 21, 220, 221 )
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> > > > > ( 22, 120, 122 )
> > > > >
> > > > > ( 23, 264, 265 )
> > > > >
> > > > > ( 24, 32, 40 )
> > > > > ( 24, 45, 51 )
> > > > > ( 24, 70, 74 )
> > > > > ( 24, 143, 145 )
> > > > >
> > > > > ( 25, 60, 65 )
> > > > > ( 25, 312, 313 )
> > > > >
> > > > > ( 26, 168, 170 )
> > > > >
> > > > > ( 27, 36, 45 )
> > > > > ( 27, 120, 123 )
> > > > > ( 27, 364, 365 )
> > > > >
> > > > > ( 28, 45, 53 )
> > > > > ( 28, 96, 100 )
> > > > > ( 28, 195, 197 )
> > > > >
> > > > > ( 29, 420, 421 )
> > > > >
> > > > > ( 30, 40, 50 )
> > > > > ( 30, 72, 78 )
> > > > > ( 30, 224, 226 )
> > > > >
> > > > > ( 31, 480, 481 )
> > > > >
> > > > > ( 32, 60, 68 )
> > > > > ( 32, 126, 130 )
> > > > > ( 32, 255, 257 )
> > > > >
> > > > > ( 33, 44, 55 )
> > > > > ( 33, 56, 65 )
> > > > > ( 33, 180, 183 )
> > > > > ( 33, 544, 545 )
> > > > >
> > > > > ( 34, 288, 290 )
> > > > >
> > > > > ( 35, 84, 91 )
> > > > > ( 35, 120, 125 )
> > > > > ( 35, 612, 613 )
> > > > >
> > > > > ( 36, 48, 60 )
> > > > > ( 36, 77, 85 )
> > > > > ( 36, 105, 111 )
> > > > > ( 36, 160, 164 )
> > > > > ( 36, 323, 325 )
> > > > >
> > > > > ( 37, 684, 685 )
> > > > >
> > > > > ( 38, 360, 362 )
> > > > >
> > > > > ( 39, 52, 65 )
> > > > > ( 39, 80, 89 )
> > > > > ( 39, 252, 255 )
> > > > > ( 39, 760, 761 )
> > > > >
> > > > > ( 40, 42, 58 )
> > > > > ( 40, 75, 85 )
> > > > > ( 40, 96, 104 )
> > > > > ( 40, 198, 202 )
> > > > > ( 40, 399, 401 )
> > > > >
> > > > > ( 41, 840, 841 )
> > > > >
> > > > > ( 42, 56, 70 )
> > > > > ( 42, 144, 150 )
> > > > > ( 42, 440, 442 )
> > > > >
> > > > > ( 43, 924, 925 )
> > > > >
> > > > > ( 44, 117, 125 )
> > > > > ( 44, 240, 244 )
> > > > > ( 44, 483, 485 )
> > > > >
> > > > > ( 45, 60, 75 )
> > > > > ( 45, 108, 117 )
> > > > > ( 45, 200, 205 )
> > > > > ( 45, 336, 339 )
> > > > > ( 45, 1012, 1013 )
> > > > >
> > > > > ( 46, 528, 530 )
> > > > >
> > > > > ( 47, 1104, 1105 )
> > > > >
> > > > > ( 48, 55, 73 )
> > > > > ( 48, 64, 80 )
> > > > > ( 48, 90, 102 )
> > > > > ( 48, 140, 148 )
> > > > > ( 48, 189, 195 )
> > > > > ( 48, 286, 290 )
> > > > > ( 48, 575, 577 )
> > > > >
> > > > > ( 49, 168, 175 )
> > > > > ( 49, 1200, 1201 )
> > > > >
> > > > > ( 50, 120, 130 )
> > > > > ( 50, 624, 626 )
> > > > >
> > > > > ( 51, 68, 85 )
> > > > > ( 51, 140, 149 )
> > > > > ( 51, 432, 435 )
> > > > > ( 51, 1300, 1301 )
> > > > >
> > > > > ( 52, 165, 173 )
> > > > > ( 52, 336, 340 )
> > > > > ( 52, 675, 677 )
> > > > >
> > > > > ( 53, 1404, 1405 )
> > > > >
> > > > > ( 54, 72, 90 )
> > > > > ( 54, 240, 246 )
> > > > > ( 54, 728, 730 )
> > > > >
> > > > > ( 55, 132, 143 )
> > > > > ( 55, 300, 305 )
> > > > > ( 55, 1512, 1513 )
> > > > >
> > > > > ( 56, 90, 106 )
> > > > > ( 56, 105, 119 )
> > > > > ( 56, 192, 200 )
> > > > > ( 56, 390, 394 )
> > > > > ( 56, 783, 785 )
> > > > >
> > > > > ( 57, 76, 95 )
> > > > > ( 57, 176, 185 )
> > > > > ( 57, 540, 543 )
> > > > > ( 57, 1624, 1625 )
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> > > > > ( 58, 840, 842 )
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> > > > > ( 59, 1740, 1741 )
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> > > > > ( 60, 63, 87 )
> > > > > ( 60, 80, 100 )
> > > > > ( 60, 91, 109 )
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> > > > > ( 60, 175, 185 )
> > > > > ( 60, 221, 229 )
> > > > > ( 60, 297, 303 )
> > > > > ( 60, 448, 452 )
> > > > > ( 60, 899, 901 )
> > > > >
> > > > > ( 61, 1860, 1861 )
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> > > > > ( 62, 960, 962 )
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> > > > > ( 63, 216, 225 )
> > > > > ( 63, 280, 287 )
> > > > > ( 63, 660, 663 )
> > > > > ( 63, 1984, 1985 )
> > > > >
> > > > > ( 64, 120, 136 )
> > > > > ( 64, 252, 260 )
> > > > > ( 64, 510, 514 )
> > > > > ( 64, 1023, 1025 )
> > > > >
> > > > > ( 65, 72, 97 )
> > > > > ( 65, 156, 169 )
> > > > > ( 65, 420, 425 )
> > > > > ( 65, 2112, 2113 )
> > > > >
> > > > > ( 66, 88, 110 )
> > > > > ( 66, 112, 130 )
> > > > > ( 66, 360, 366 )
> > > > > ( 66, 1088, 1090 )
> > > > >
> > > > > ( 67, 2244, 2245 )
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> > > > > ( 68, 285, 293 )
> > > > > ( 68, 576, 580 )
> > > > > ( 68, 1155, 1157 )
> > > > >
> > > > > ( 69, 92, 115 )
> > > > > ( 69, 260, 269 )
> > > > > ( 69, 792, 795 )
> > > > > ( 69, 2380, 2381 )
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> > > > > ( 70, 168, 182 )
> > > > > ( 70, 240, 250 )
> > > > > ( 70, 1224, 1226 )
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> > > > > ( 71, 2520, 2521 )
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> > > > > ( 72, 96, 120 )
> > > > > ( 72, 135, 153 )
> > > > > ( 72, 154, 170 )
> > > > > ( 72, 210, 222 )
> > > > > ( 72, 320, 328 )
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> > > > > ( 72, 646, 650 )
> > > > > ( 72, 1295, 1297 )
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> > > > > ( 73, 2664, 2665 )
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> > > > > ( 74, 1368, 1370 )
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> > > > > ( 75, 100, 125 )
> > > > > ( 75, 180, 195 )
> > > > > ( 75, 308, 317 )
> > > > > ( 75, 560, 565 )
> > > > > ( 75, 936, 939 )
> > > > > ( 75, 2812, 2813 )
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> > > > > ( 76, 357, 365 )
> > > > > ( 76, 720, 724 )
> > > > > ( 76, 1443, 1445 )
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> > > > > ( 77, 264, 275 )
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> > > > > ( 77, 2964, 2965 )
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> > > > > ( 78, 104, 130 )
> > > > > ( 78, 160, 178 )
> > > > > ( 78, 504, 510 )
> > > > > ( 78, 1520, 1522 )
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> > > > > ( 79, 3120, 3121 )
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> > > > > ( 80, 84, 116 )
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> > > > > ( 80, 192, 208 )
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> > > > >
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> > > > > ( 84, 245, 259 )
> > > > > ( 84, 288, 300 )
> > > > > ( 84, 437, 445 )
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> > > > > ( 85, 720, 725 )
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> > > > > ( 86, 1848, 1850 )
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> > > > > ( 87, 116, 145 )
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> > > > >
> > > > > ( 88, 105, 137 )
> > > > > ( 88, 165, 187 )
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> > > > > ( 88, 966, 970 )
> > > > > ( 88, 1935, 1937 )
> > > > >
> > > > > ( 89, 3960, 3961 )
> > > > >
> > > > > ( 90, 120, 150 )
> > > > > ( 90, 216, 234 )
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> > > > > ( 90, 672, 678 )
> > > > > ( 90, 2024, 2026 )
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> > > > > ( 91, 312, 325 )
> > > > > ( 91, 588, 595 )
> > > > > ( 91, 4140, 4141 )
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> > > > > ( 92, 525, 533 )
> > > > > ( 92, 1056, 1060 )
> > > > > ( 92, 2115, 2117 )
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> > > > > ( 93, 124, 155 )
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> > > > > ( 93, 1440, 1443 )
> > > > > ( 93, 4324, 4325 )
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> > > > >
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> > > > > ( 1005, 101000, 101005 )
> > > > > ( 1005, 168336, 168339 )
> > > > > ( 1005, 505012, 505013 )
> > > > >
> > > > >
> > > > > ( 9999, 13332, 16665 )