Take an arbitrary quadrangle and divide each of the four sides into three
equal parts. Draw the lines through adjacent dividing points.
The result is a parallelogram. This theorem is due to
F. Wittenbauer
(around
1900).
Figure: w130150a
The centre of the parallelogram is the
centroid
(centre of mass) of the
lamina
(plate of uniform density) defined by the original quadrangle.