Geodesic
Klein's Erlangen Program and geometry of a triangle
Matematičeskoe obrazovanie, Tome 83 (2017) no. 3, pp. 28-42

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

In this article is compared triangle's geometry and Felix Klein's Erlangen Program. As a result it revealed mistake wide-spread interpretation Euclid's planimetry as the doctrine about invariants of group motions of plane. Author considers one of possible ways of removal this mistake with the help
Keywords: the Steiner curve, the group of transformations, the group on the set of triangles, the group of motions, the affine and projective transformations, the group of point transformations, the group of linear fractional transformations, the orthopole points of the tangents to the circumscribed circle form a Steiner curve. 
@article{MO_2017_83_3_a3,
     author = {M. E. Stepanov},
     title = {Klein's {Erlangen} {Program} and geometry of a triangle},
     journal = {Matemati\v{c}eskoe obrazovanie},
     pages = {28--42},
     publisher = {mathdoc},
     volume = {83},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MO_2017_83_3_a3/}
}
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M. E. Stepanov. Klein's Erlangen Program and geometry of a triangle. Matematičeskoe obrazovanie, Tome 83 (2017) no. 3, pp. 28-42. http://geodesic.mathdoc.fr/item/MO_2017_83_3_a3/