Difference between revisions of "Wittenbauer theorem"
From Encyclopedia of Mathematics
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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> | + | <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> | ||
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
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