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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