Assuming the side is a rectangle, draw diagonals (lines from alternate
corners), and the point of intersection will be the center of the side.
There are several ways to extend it to the length of the side--using a
compass to "bisect an angle" comes to mind. I imagine that construction
is explained in more than one place on the web.
A waiter/magician once showed me how to balance a tray... put the
board on three fingers, slowly move the fingers in toward the center,
the trick is to allow the tray to slide so that the finger that moves is
the one carrying the least weight. when the weight is even on all
points, and they are fairly close together, the balance point emerges.
If you had three fairly accurate scales, like powder scales, you could
set it on three pins, and adjust until all three balances read the same.
Then draw the triangle between the three points, bisect each leg of
that triangle, and where the bisectors cross ought to be the center of mass.
Maybe square it off?
1. measure max width and cut 2 small pieces of wood with length = max width
2. put one of those pieces at each end of the oblong and two more pieces
along the sides of the oblong making sure all four pieces are square.
That should allow you to connect the center points of the two pieces from
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