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Mathematical Education, 2017, Issue 3(83), Pages 28–42 (Mi mo612)  
Students and teachers of mathematical specialties

Klein's Erlangen Program and geometry of a triangle

M. E. Stepanov

Moscow State University of Psychology and Education
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Abstract: 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.
Document Type: Popular science or education materials
UDC: 514.1
Language: Russian
Citation: M. E. Stepanov, “Klein's Erlangen Program and geometry of a triangle”, Math. Ed., 2017, no. 3(83), 28–42
Citation in format AMSBIB
\Bibitem{Ste17}
\by M.~E.~Stepanov
\paper Klein's Erlangen Program and geometry of a triangle
\jour Math. Ed.
\yr 2017
\issue 3(83)
\pages 28--42
\mathnet{http://mi.mathnet.ru/mo612}
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