There's a discussion of this problem here: 
https://math.stackexchange.com/questions/1971097/what-are-the-axes-of-an-ellipse-within-a-rhombus/1971327#1971327

  They note that there are an infinite number of ellipses that you can 
inscribe, so there isn't a unique answer unless you add another criteria.


On 6/5/2018 9:55 AM, Bald Eagle wrote:
>
> I was modeling something the other day and wanted to autopmate the placement of
> some pegs, and thought that finding the foci of an ellipse that's inscribed in
> the region common to two overlapping boards would be a good way to place them.
>
> No idea how to do it yet.
>
> Take two boards - say 15 units x 1 unit, overlap them at 90 deg, you get a 1 by
> 1 unit square.  Rotate 90 deg, and you fully align them to get 15 x 1 unit
> rectangle.  Somewhere in the middle you get a lot of diamonds/rhombi/etc.
>
> Even just finding a function for the max and min  vertical positions of the
> overlapping region of the boards seemed an interesting problem.
>
> Just far too many things to do IRL at the moment.
> I thought perhaps someone would like to ponder the puzzle(s).  :)
>

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