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Difference between revisions of "Wittenbauer theorem"

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<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  H.S.M. Coxeter,  "Introduction to geometry" , Wiley  (1969)  pp. 216</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top">  W. Blaschke,  "Projektive Geometrie" , Birkhäuser  (1954)  pp. 13</TD></TR></table>
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<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>
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<TR><TD valign="top">[a2]</TD> <TD valign="top">  W. Blaschke,  "Projektive Geometrie" , Birkhäuser  (1954)  pp. 13</TD></TR>
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Revision as of 15:14, 16 April 2018

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://encyclopediaofmath.org/index.php?title=Wittenbauer_theorem&oldid=16327
This article was adapted from an original article by M. Hazewinkel (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article