Analysis of the Pythagorean Theorem


Edward F. Block IV, Ph.D.
Updated September 2006

C x C equals A x A + B x B

C_____C x C_____A_____A x A_____B_____B x B
000000
11----
24-2-2
39----
416-8-8
52539416
636----
749----
864----
981----
10100636864
11121----
12144----
1316952512144
14196----
1522598112144
16256----
1728986415225
18324----
19361----
204001214416256
21441----
22484----
23529----
24576----
2562574924576
--1522520400
266761010024576
27729----
28784----
298412040021441
309001832424576
31961----
321024----
331089----
3411561625630900
3512252144128784
361296----
3713691214435225
381444----
39152115225361296
40160024576321024
411681981401600
421764----
431849----
441936----
45202527729361296
462116----
472209----
482304----
492401----
50250030900401600
51260124576452025
52270420400482304
53280928784452025
542916----
553025331089441936
563136----
573249----
583364401600421764
593481----
603600361296482304
61372111121603600
623844----
633969----
644096----
65422516256633969
--25625603600
--331089563136
--391521522704
664356----
674489----
684624321024603600
694761----
704900421764563136
715041----
725184----
735329482304553025
74547624576704900
75562521441725184
-452025603600
765776----
775929----
78608430900725184
796241----
806400482304644096
816561----
82672418324806400
836889----
847056----
85722513169847056
--361296775929
--401600755625
--512601684624
867396----
877569603600633969
887744----
897921----
908100542916725184
918281351225847056
928464----
938649----
948836----
959025573249765776
969216----
979409654225725184
989604----
999801----
10010000603600806400

Numbers utilized: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 18, 20, 21, 24,
25, 27, 18, 29, 30, 32, 33, 35, 36, 39, 40, 42, 44, 45, 48, 51, 52, 54, 55, 56,
57, 60, 63, 64, 65, 68, 70, 72, 75, 76, 77, 80, 84.

Numbers not utilized: 0, 1, 14, 17, 19, 22, 23, 26, 29, 31, 34, 37, 38, 41, 43,
46, 47, 49, 50, 53, 58, 59, 61, 62, 66, 67 69, 71, 73, 74, 78, 79, 81, 82, 83.

Multiples of 10: 5 & 50, 10 & 100

Numbers with the most internal sets of squares: 65, 85.

Longest sequential number series is 4: 50, 51, 52, 53.

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