# Wittenbauer theorem

From Encyclopedia of Mathematics

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.

#### References

[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: http://www.encyclopediaofmath.org/index.php?title=Wittenbauer_theorem&oldid=43171

This article was adapted from an original article by M. Hazewinkel (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article