Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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SHARYGIN TRIANGLES AND ELLIPTIC CURVES

  • Netay, Igor V. (Institute for Information Transmission Problems, RAS) ;
  • Savvateev, Alexei V. (Dmitry Pozharsky University Moscow Institute of Physics and Technology New Economic School)
  • Received : 2016.08.17
  • Accepted : 2017.02.24
  • Published : 2017.09.30
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Abstract

The paper is devoted to the description of family of scalene triangles for which the triangle formed by the intersection points of bisectors with opposite sides is isosceles. We call them Sharygin triangles. It turns out that they are parametrized by an open subset of an elliptic curve. Also we prove that there are infinitely many non-similar integer Sharygin triangles.

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Acknowledgement

Supported by : Russian Foundation for Sciences, Ministry of Education and Science of the Russian Federation

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