Geodesic
Elementary proof of Steinharz hypothesis
Matematičeskoe obrazovanie, Tome 75 (2015) no. 3, pp. 2-13.

Voir la notice de l'article provenant de la source Math-Net.Ru

Let a triangle be divided in six smaller triangles by bisectors. The Steinharz hypothesis claims that the centers of the incircles of these six triangles belong to an ellipsis. The authors suggest an elementary proof.
Keywords: subdivision of a triangle by its bysectors, centers of the incircles of the subdivision triangles, the common ellipsis of the centers. 
@article{MO_2015_75_3_a0,
     author = {O. R. Kayumov and K. E. Kashirina},
     title = {Elementary proof of {Steinharz} hypothesis},
     journal = {Matemati\v{c}eskoe obrazovanie},
     pages = {2--13},
     publisher = {mathdoc},
     volume = {75},
     number = {3},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MO_2015_75_3_a0/}
}
TY  - JOUR
AU  - O. R. Kayumov
AU  - K. E. Kashirina
TI  - Elementary proof of Steinharz hypothesis
JO  - Matematičeskoe obrazovanie
PY  - 2015
SP  - 2
EP  - 13
VL  - 75
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MO_2015_75_3_a0/
LA  - ru
ID  - MO_2015_75_3_a0
ER  - 
%0 Journal Article
%A O. R. Kayumov
%A K. E. Kashirina
%T Elementary proof of Steinharz hypothesis
%J Matematičeskoe obrazovanie
%D 2015
%P 2-13
%V 75
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MO_2015_75_3_a0/
%G ru
%F MO_2015_75_3_a0
O. R. Kayumov; K. E. Kashirina. Elementary proof of Steinharz hypothesis. Matematičeskoe obrazovanie, Tome 75 (2015) no. 3, pp. 2-13. http://geodesic.mathdoc.fr/item/MO_2015_75_3_a0/

[1] L. A. Shteingarts, “Gipotezy o medianakh, vysotakh, bissektrisakh i ...ellipsakh”, Matematicheskoe obrazovanie, 2012, no. 2(62), 41–48

[2] L. A. Shteingarts, “Orbity Zhukova i teorema Morleya”, Matematika v shkole, 2012, no. 6, 53-61

[3] D. S. Grigorev, A. G. Myakishev, “I snova o gipotezakh Shteingartsa”, Matematicheskoe obrazovanie, 2013, no. 3(67), 40–56

[4] N. N. Osipov, “O mekhanicheskom dokazatelstve planimetricheskikh teorem ratsionalnogo tipa”, Programmirovanie, 40:2 (2014), 41–50

[5] V. I. Arnold, Gyuigens i Barrou, Nyuton i Guk, Nauka, M., 1989

[6] O. R. Kayumov, Proektivnye svoistva figur, Izd-vo OmGPU, Omsk, 2003