Sharygin triangles and elliptic curves
Bull. Korean Math. Soc. 2017 Vol. 54, No. 5, 1597-1617
https://doi.org/10.4134/BKMS.b160681
Published online September 30, 2017
Igor V. Netay, Alexei V. Savvateev
National Research University Higher School of Economics, New Economic School
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.
Keywords : elliptic curve, Diophantine equation, plane geometry
MSC numbers : 11D25, 14H45, 97G40
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