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Egypt
Origins

Ancient Semitic Plimpton 322

with Calculated Parameters for Pythagorean Triplets
and Integral Solution to Circle Equation

 

hLine y x a m n m/n y/x Θ a/y
1 120 119 169 12 5 2.40 1.0084 45.2 1.408
2 3456 3367 4825 64 27 2.37 1.0264 45.8 1.396
3 4800 4601 6649 75 32 2.34 1.0433 46.2 1.385
4 13,500 12,709 18,541 125 54 2.32 1.0622 46.8 1.373
5 72 65 97 9 4 2.25 1.1077 47.9 1.347
6 360 319 481 20 9 2.22 1.1285 48.4 1.336
7 2700 2291 3541 54 25 2.16 1.1785 49.7 1.311
8 960 799 1249 32 15 2.13 1.2015 50.2 1.301
9 600 481 769 25 12 2.09 1.2474 51.3 1.282
10 6480 4961 8161 81 40 2.03 1.3062 52.6 1.259
11 60 45 75 2 1 2.00 1.3300 53.2 1.250
12 2400 1679 2929 48 25 1.92 1.4294 55.0 1.220
13 240 161 289 15 8 1.88 1.4907 56.2 1.204
14 2700 1771 3229 50 27 1.85 1.5246 56.5 1.196
15 90 56 106 9 5 1.80 1.6071 58.2 1.178

 

Plimpton 322 According to Robson
Calculated Values of Ratios
Robson Insertions Shown in Bold Face

Line
No.
x 1/x (x - 1/x)/2
S/L
(x + 1/x)/2
D/L
[(x + 1/x)/2]2 Angle
1 2.400000000 0.416666667 0.991666667 1.40833333 1.98340278 44.7603
2 2.370370370 0.421875000 0.974247685 1.39612269 1.94915855 44.2527
3 2.343749990 0.426666668 0.958541661 1.38520833 1.91880212 43.7873
4 2.314814810 0.432000001 0.941407405 1.37340741 1.88624790 43.2713
4a 2.304000000 0.434027778 0.934986111 1.36901389 1.87419903 43.0756
5 2.250000000 0.444444444 0.902777778 1.34722222 1.81500772 42.0750
6 2.222222220 0.450000000 0.886111110 1.33611111 1.78519290 41.5445
6a 2.170138888 0.460800000 0.854669444 1.31546944 1.73045986 40.5195
7 2.160000000 0.462962963 0.848518519 1.31148148 1.71998368 40.3152
8 2.133333330 0.468750001 0.832291665 1.30104167 1.69270942 39.7703
8a 2.109375000 0.474074074 0.817650463 1.29172454 1.66855228 39.2712
9 2.083333330 0.480000001 0.801666665 1.28166667 1.64266944 38.7180
9a 2.048000000 0.488281250 0.779859375 1.26814063 1.60818064 37.9492
10 2.025000000 0.493827160 0.765586420 1.25941358 1.58612257 37.4372
11 2.000000000 0.500000000 0.750000000 1.25000000 1.56250000 36.8699
11a 1.953125000 0.512000000 0.720562500 1.23256250 1.51921032 35.7751
12 1.920000000 0.520833333 0.699583333 1.22041667 1.48941684 34.9760
12a 1.896296290 0.527343752 0.684476269 1.21182002 1.46850776 34.3907
13 1.875000000 0.533333333 0.670833333 1.20416667 1.45001736 33.8550
14 1.851851850 0.540000001 0.655925925 1.19592593 1.43023882 33.2619
15 1.800000000 0.555555556 0.622222222 1.17777778 1.38716049 31.8908

 

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