Before tackling this one, take a look at
this one.
+D
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+A
A, B, C and D are nonadjacent vertices of a cube. There is a point P in space such that PA=3, PB=5, PC=7, and PD=6. Find the distance from P to the other four vertices and find the length of the edge of the cube.
There are two answers, one with P outside the cube and one with P inside the cube.
(In reply to
Heuristic computer solution for modified problem by Charlie)
If PD is reduced to 6, we seem to be able to get an internal point:
x y z size
2.881 4.065 0.421; 5.4880 3.0000 5.0000 7.0000 6.0000
as well as an external point
x y z size
1.787 3.891 2.581; 3.0898 3.0003 5.0000 7.0000 6.0000
(The choice of internal or external point can be influenced by the choice of initial randomization limits.)

Posted by Charlie
on 20040718 20:18:01 