Geodesic
On hypotheses by L.~Steingarts
Matematičeskoe obrazovanie, Tome 67 (2013) no. 3, pp. 40-56.

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

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. 
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D. S. Grigoryev; A. G. Myakishev. On hypotheses by L.~Steingarts. Matematičeskoe obrazovanie, Tome 67 (2013) no. 3, pp. 40-56. http://geodesic.mathdoc.fr/item/MO_2013_67_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 <ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=925008'>925008</ext-link>

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

[4] Malyshev I., “Trigonometricheskie formuly v treugolnike i ikh obobscheniya”, Fraktal: elektronnyi zhurnal, 2013, no. 1 <ext-link ext-link-type='uri' href='http://www.schoolpress.ru/products/rubria/index.php?ID=46934&amp;SECTION_ID=913'>http://www.schoolpress.ru/products/rubria/index.php?ID=4693SECTION_ID=913</ext-link>

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

[6] Myakishev A., “Konfiguratsiya ravenstva”, Matematicheskoe obrazovanie, 2008, no. 2(46), 29–44 <ext-link ext-link-type='uri' href='http://www.geometry.ru/persons/myakishev/text.htm'>http://www.geometry.ru/persons/myakishev/text.htm</ext-link>

[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, <ext-link ext-link-type='uri' href='http://faculty.evansville.edu/ck6/encyclopedia/'>http://faculty.evansville.edu/ck6/encyclopedia/</ext-link>

[10] Myakishev A., Woo P., “On the Circumcenters of Cevasix Configurations”, Forum Geometricorum, 2003, no. 3 <ext-link ext-link-type='uri' href='http://forumgeom.fau.edu/FG2003volume3/FG200305index.html'>http://forumgeom.fau.edu/FG2003volume3/FG200305index.html</ext-link><ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=2004109'>2004109</ext-link>

[11] Yiu P., Introduction to the Geometry of the Triangle, <ext-link ext-link-type='uri' href='http://math.fau.edu/yiu/GeometryNotes020402.pdf'>http://math.fau.edu/yiu/GeometryNotes020402.pdf</ext-link>