Difference between revisions of "Wittenbauer theorem"
From Encyclopedia of Mathematics
m (→References: isbn link) |
m |
||
| Line 8: | Line 8: | ||
====References==== | ====References==== | ||
| − | + | * {{Ref|a1}} H.S.M. Coxeter, "Introduction to geometry" (2nd ed.), Wiley (1969) pp. 216 {{ZBL|0181.48101}}; (repr.1989) {{ISBN|0-471-50458-0}} | |
| − | + | * {{Ref|a2}} W. Blaschke, "Projektive Geometrie", Birkhäuser (1954) pp. 13 {{ZBL|0057.12706}} | |
| − | |||
| − | |||
{{OldImage}} | {{OldImage}} | ||
Latest revision as of 07:23, 31 July 2025
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 Zbl 0057.12706
🛠️ This page contains images that should be replaced by better images in the SVG file format. 🛠️
How to Cite This Entry:
Wittenbauer theorem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Wittenbauer_theorem&oldid=56166
Wittenbauer theorem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Wittenbauer_theorem&oldid=56166
This article was adapted from an original article by M. Hazewinkel (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article