Take a right triangle with integer sides A, B, & C.
(C need not be the hypotenuse.)
To side C attach another right triangle with integer sides C, D & E.
On this new triangle attach another right triangle to either side D or E. Continue the process of attaching a new right triangle to the previous; creating a chain of right triangles.
Three further rules:
1. No side length may be repeated.
2. No triangles may overlap.
3. No side may have length over 10000.
How many triangles can you make in this chain?
A computer program comes up with 12471 Pythagorean triples--too many to list here--starting with 3-4-5 and ending with 6000-8000-10000.
3 4 5
6 8 10
5 12 13
9 12 15
8 15 17
12 16 20
7 24 25
15 20 25
10 24 26
20 21 29
18 24 30
16 30 34
21 28 35
12 35 37
15 36 39
24 32 40
9 40 41
27 36 45
14 48 50
...
5988 7984 9980
1269 9900 9981
3417 9380 9983
3840 9216 9984
1575 9860 9985
4656 8833 9985
5991 7988 9985
6943 7176 9985
5890 8064 9986
6237 7800 9987
3078 9504 9990
3240 9450 9990
5616 8262 9990
5994 7992 9990
6695 7416 9991
6392 7680 9992
5997 7996 9995
4704 8820 9996
2772 9605 9997
3845 9228 9997
4795 8772 9997
6253 7800 9997
1980 9801 9999
2800 9600 10000
3520 9360 10000
5376 8432 10000
6000 8000 10000
Edited on March 20, 2006, 4:20 pm
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Posted by Charlie
on 2006-03-20 16:15:15 |
No Subject
