[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.b160681

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)

Publication Information

Bulletin of the Korean Mathematical Society / v.54, no.5, 2017 , pp. 1597-1617 More about this Journal

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;

Citations & Related Records

Reference

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