11Z05 — 1 articles found.

Further Remarks on Rational Albime Triangles

C. R. Math. Rep. Acad. Sci. Canada Vol. 39 (2) 2017, pp. 67-76
Vol.39 (2) 2017
Jasbir S. Chahal; Josselin Kooij; Jaap Top Details
(Received: 2015-07-26 , Revised: 2016-11-14 )
(Received: 2015-07-26 , Revised: 2016-11-14 )

Jasbir S. Chahal,Department of Mathematics, Brigham Young University, Provo, UT 84602, USA; e-mail: jasbir@math.byu.edu

Josselin Kooij,University of Groningen, Department of Mathematics, P.O. Box 407, 9700 AK, Groningen, The Netherlands; e-mail: j.f.kooij@student.rug.nl

Jaap Top,University of Groningen, Department of Mathematics, P.O. Box 407, 9700 AK, Groningen, The Netherlands; e-mail: j.top@rug.nl

Abstract/Résumé:

In this note we present further number theoretic properties of the rational albime triangles, in particular, the distribution of acute vs. obtuse rational albime triangles. The notion of albime triangle is extended to include the case of external angle bisector. The proportion of internal vs. external rational albime triangles is also computed.

Dans cette note, nous présentons des propriétés supplémentaires (concernant la théorie des nombres) des triangles rationnels ‘albimes’; en particulier, la distribution des triangles rationnels albimes aigus contre obtus. La notion de triangle albime est développé pour comprendre le cas d’extérieur bissectrice. On calcule aussi la proportion des triangles rationnels albimes internes contre externes.

Keywords: Ceva's theorem, elliptic curves, primitive albime triplets, rational albime triangles

AMS Subject Classification: Elliptic curves over global fields, Miscellaneous applications of number theory 11G05, 11Z05

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