View source for Wittenbauer theorem

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).

<img style="border:1px solid;" src="https://www.encyclopediaofmath.org/legacyimages/common_img/w130150a.gif" />

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.

====References====
<table>
<TR><TD valign="top">[a1]</TD> <TD valign="top">  H.S.M. Coxeter,   "Introduction to geometry" (2nd ed.), Wiley  (1969)  pp. 216  {{ZBL|0181.48101}}; (repr.1989) ISBN  0-471-50458-0</TD></TR>
<TR><TD valign="top">[a2]</TD> <TD valign="top">  W. Blaschke,   "Projektive Geometrie" , Birkhäuser  (1954)  pp. 13</TD></TR>
</table>