Howell, Leonard W. (MSFC-VP62) wrote:
> I didn't have much luck solving this one on my own but found the
> solution at mathworld.
>
> Can you explain how it was solved, hopefully with some J thinking?
>

Here's my solution, with no J thinking.

Spoiler below....


















This method gives the result: maybe it does not show it is actually
the largest square.

For some 0<x<1, take vertices

(x,0,0)
(0,x,0)
(1,1-x,1)
(1-x,1,1)

Calculating the square of the side in two ways gives

2x^2=2(1-x)^2+1,

so x=3/4, and the side of the square is 3%2*%:2=1.06066.

Best wishes,

John

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