On hypotheses by L. Steingarts
Matematičeskoe obrazovanie, no. 3 (2013), pp. 40-56 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Professor L.Steingarts has launched several hypotheses that some specially constructed points of a triangle belong to one quadratic curve. Some of these hypotheses are denied and some are proven in the paper.
Keywords: Shteingart hypothesis of an ellipse connected with conic triangle, barycentric coordinates, special cases.
@article{MO_2013_3_a3,
     author = {D. S. Grigoryev and A. G. Myakishev},
     title = {On hypotheses by {L.~Steingarts}},
     journal = {Matemati\v{c}eskoe obrazovanie},
     pages = {40--56},
     year = {2013},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MO_2013_3_a3/}
}
TY  - JOUR
AU  - D. S. Grigoryev
AU  - A. G. Myakishev
TI  - On hypotheses by L. Steingarts
JO  - Matematičeskoe obrazovanie
PY  - 2013
SP  - 40
EP  - 56
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/MO_2013_3_a3/
LA  - ru
ID  - MO_2013_3_a3
ER  - 
%0 Journal Article
%A D. S. Grigoryev
%A A. G. Myakishev
%T On hypotheses by L. Steingarts
%J Matematičeskoe obrazovanie
%D 2013
%P 40-56
%N 3
%U http://geodesic.mathdoc.fr/item/MO_2013_3_a3/
%G ru
%F MO_2013_3_a3
D. S. Grigoryev; A. G. Myakishev. On hypotheses by L. Steingarts. Matematičeskoe obrazovanie, no. 3 (2013), pp. 40-56. http://geodesic.mathdoc.fr/item/MO_2013_3_a3/

[1] Akopyan A., Zaslavskii A., Geometricheskie svoistva krivykh vtorogo poryadka, MTsNMO, M., 2011

[2] Balk M., Boltyanskii V., Geometriya mass, Nauka, M., 1987 | MR

[3] Zaslavskii A., Geometricheskie preobrazovaniya, MTsNMO, M., 2004

[4] Malyshev I., “Trigonometricheskie formuly v treugolnike i ikh obobscheniya”, Fraktal: elektronnyi zhurnal, 2013, no. 1 http://www.schoolpress.ru/products/rubria/index.php?ID=4693SECTION_ID=913

[5] Myakishev A., Elementy geometrii treugolnika, MTsNMO, M., 2009

[6] Myakishev A., “Konfiguratsiya ravenstva”, Matematicheskoe obrazovanie, 2008, no. 2(46), 29–44 http://www.geometry.ru/persons/myakishev/text.htm

[7] Prasolov V., Zadachi po planimetrii, MTsNMO, M., 2007

[8] Sharygin I., Geometriya. Planimetriya: zadachnik 9–11, Drofa, M., 2001

[9] Kimberling C., Encyclopedia of Triangle Centers, http://faculty.evansville.edu/ck6/encyclopedia/

[10] Myakishev A., Woo P., “On the Circumcenters of Cevasix Configurations”, Forum Geometricorum, 2003, no. 3 http://forumgeom.fau.edu/FG2003volume3/FG200305index.html | MR

[11] Yiu P., Introduction to the Geometry of the Triangle, http://math.fau.edu/yiu/GeometryNotes020402.pdf