Wittenbauer theorem

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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.


[a1] H.S.M. Coxeter, "Introduction to geometry" (2nd ed.), Wiley (1969) pp. 216 Zbl 0181.48101; (repr.1989) ISBN 0-471-50458-0
[a2] W. Blaschke, "Projektive Geometrie" , Birkhäuser (1954) pp. 13
How to Cite This Entry:
Wittenbauer theorem. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by M. Hazewinkel (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article