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).
The centre of the parallelogram is the centroid (centre of mass) of the lamina (plate of uniform density) defined by the original quadrangle.
|[a1]||H.S.M. Coxeter, "Introduction to geometry" , Wiley (1969) pp. 216|
|[a2]||W. Blaschke, "Projektive Geometrie" , Birkhäuser (1954) pp. 13|
Wittenbauer theorem. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Wittenbauer_theorem&oldid=16327