Van Obel's theorem ( Van Aubel [1] or, in some sources, Van Obel [2] ) —the theorem of the Flemish mathematician Van Aubel (or van Obele, Henricus Hubertus van Aubel) proved in 1878. [3] .
This is a particular case of the Peter – Douglas – Neumann theorem [1] , and Tebo’s theorem follows from its very own theorem .
Content
Formulation
The theorem can be applied to self-intersecting quadrangles.
If on the sides of an arbitrary non-self-intersecting quadrilateral to construct squares externally and connect the centers of the opposite, then the resulting segments will be equal and perpendicular . (See pic.)
Literature
- van Aubel, HH "Note concernant les centers de carrés construits sur les côtés d'un polygon quelconque." Nouv. Corresp. Math 4, 40-44, 1878. (Fr.)
- Ponarin Ya. P. Elementary geometry. In 2 t. - Moscow : ICNMO , 2004. - p. 24. - ISBN 5-94057-170-0 .
- Dm Yefremov New Triangle Geometry 1902
- Zetel S.I. The new geometry of the triangle. M: Uchpedgiz, 1962. 153 p.
Notes
- ↑ 1 2 Weisstein, Eric W. van Aubel's Theorem (Eng.) On Wolfram MathWorld .
- ↑ Van Obel Theorem and Barycentric coordinates . Author - Alexander Bogomolny (eng.)
- ↑ HH van Aubel, (1878), “Note the decanting centers of the carres construits sur les côtés d'un polygon quelconque” (Fr.) , Nouvelle Correspondance Mathématique 4 , 1878, pp. 40-44
See also
- Napoleon's theorem