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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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참고문헌 (20)
참고문헌 신청
L. Bankoff / 1973 / The Heptagonal Triangle / Math. Mag 46(1):7~19
C. Breuil / 2001 / On the modularity of elliptic curves over Q : wild 3-adic exercises / J. Amer. Math. Soc 14(4):843~939
B. H. Gross / 1986 / Heegner points and derivatives of L-series / Invent. Math 84(2):225~320
R. Hartshorne / 1977 / Algebraic Geometry / Springer-Verlag
H. Hasse / 1993 / Beweis des Analogons der Riemannschen Vermutung für die Artinschen und F. K. Schmidtschen Kongruenzzetafunktionen in gewissen eliptischen Fällen. Vorläufige Mitteilung / Nachr. Ges. Wiss. Göttingen I, Math.-Phys. Kl. Fachgr. I Math. Nr 42:253~262
C. Breuil / 2001 / On the modularity of elliptic curves over Q : wild 3-adic exercises / J. Amer. Math. Soc 14(4):843~939
B. H. Gross / 1986 / Heegner points and derivatives of L-series / Invent. Math 84(2):225~320
R. Hartshorne / 1977 / Algebraic Geometry / Springer-Verlag
H. Hasse / 1993 / Beweis des Analogons der Riemannschen Vermutung für die Artinschen und F. K. Schmidtschen Kongruenzzetafunktionen in gewissen eliptischen Fällen. Vorläufige Mitteilung / Nachr. Ges. Wiss. Göttingen I, Math.-Phys. Kl. Fachgr. I Math. Nr 42:253~262
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