Generation of Pythagorean Triples from Reciprocals
First 22 Whole Numbers
(p = x, q = 2)
Note: The first three lines are not mathematically sound
|
p |
p/q |
q/p |
(p2 - q2) /2pq |
(p2 + q2) /2pq |
[(p2 + q2) /2pq]2 |
(p/q-q/p)/2 |
(p/q+q/p)/2 |
Prod |
a |
c |
b |
|
4 |
2.00 |
0.50000000 |
12.00000000 |
20.00000000 |
400.00000000 |
0.7500000000 |
1.2500000000 |
4 |
3 |
5 |
4 |
|
5 |
2.50 |
0.40000000 |
16.80000000 |
23.20000000 |
538.24000000 |
1.0500000000 |
1.4500000000 |
1 |
21 |
29 |
20 |
|
6 |
3.00 |
0.33333333 |
21.33333333 |
26.66666667 |
711.11111111 |
1.3333333333 |
1.6666666667 |
8 |
4 |
5 |
3 |
|
7 |
3.50 |
0.28571429 |
25.71428571 |
30.28571429 |
917.22448980 |
1.6071428571 |
1.8928571429 |
1 |
45 |
53 |
28 |
|
8 |
4.00 |
0.25000000 |
30.00000000 |
34.00000000 |
1156.00000000 |
1.8750000000 |
2.1250000000 |
4 |
15 |
17 |
8 |
|
9 |
4.50 |
0.22222222 |
34.22222222 |
37.77777778 |
1427.16049383 |
2.1388888889 |
2.3611111111 |
1 |
77 |
85 |
36 |
|
10 |
5 |
0.20000000 |
38.40000000 |
41.60000000 |
1730.56000000 |
2.4000000000 |
2.6000000000 |
8 |
12 |
13 |
5 |
|
11 |
5.50 |
0.18181818 |
42.54545455 |
45.45454545 |
2066.11570248 |
2.6590909091 |
2.8409090909 |
1 |
117 |
125 |
44 |
|
12 |
6.00 |
0.16666667 |
46.66666667 |
49.33333333 |
2433.77777778 |
2.9166666667 |
3.0833333333 |
4 |
35 |
37 |
12 |
|
13 |
6.50 |
0.15384615 |
50.76923077 |
53.23076923 |
2833.51479290 |
3.1730769231 |
3.3269230769 |
1 |
165 |
173 |
52 |
|
14 |
7.00 |
0.14285714 |
54.85714286 |
57.14285714 |
3265.30612245 |
3.4285714286 |
3.5714285714 |
8 |
24 |
25 |
7 |
|
15 |
7.50 |
0.13333333 |
58.93333333 |
61.06666667 |
3729.13777778 |
3.6833333333 |
3.8166666667 |
1 |
221 |
229 |
60 |
|
16 |
8.00 |
0.12500000 |
63.00000000 |
65.00000000 |
4225.00000000 |
3.9375000000 |
4.0625000000 |
4 |
63 |
65 |
16 |
|
17 |
8.50 |
0.11764706 |
67.05882353 |
68.94117647 |
4752.88581315 |
4.1911764706 |
4.3088235294 |
1 |
285 |
293 |
68 |
|
18 |
9 |
0.11111111 |
71.11111111 |
72.88888889 |
5312.79012346 |
4.4444444444 |
4.5555555556 |
8 |
40 |
41 |
9 |
|
19 |
9.50 |
0.10526316 |
75.15789474 |
76.84210526 |
5904.70914127 |
4.6973684211 |
4.8026315789 |
1 |
357 |
365 |
76 |
|
20 |
10.00 |
0.10000000 |
79.20000000 |
80.80000000 |
6528.64000000 |
4.9500000000 |
5.0500000000 |
4 |
99 |
101 |
20 |
|
21 |
10.50 |
0.09523810 |
83.23809524 |
84.76190476 |
7184.58049887 |
5.2023809524 |
5.2976190476 |
1 |
437 |
445 |
84 |
|
22 |
11.00 |
0.09090909 |
87.27272727 |
88.72727273 |
7872.52892562 |
5.4545454545 |
5.5454545455 |
8 |
60 |
61 |
11 |