IJPAM: Volume 64, No. 4 (2010)

ON THE PERIMETER OF INTEGRAL TRIANGLES

Russell A. Gordon$^1$, Jonathan M. Wells$^2$
$^{1,2}$Whitman College
345, Boyer Avenue, Walla Walla, WA 99362, USA
$^1$e-mail: [email protected]
$^2$e-mail: [email protected]


Abstract.Given a triangle with relatively prime integral sides and a $\theta$ degree angle, let $C(n)$ denote the number of such triangles with perimeter less than or equal to $n$. We consider the asymptotic behavior of the function $C(n)/n$ when $\theta$ has the values $60$, $90$, and $120$, and thus extend known results for $90$ degree triangles to $60$ degree and $120$ degree triangles. The paper is written in such a way that readers with a minimal background in number theory can follow the details of the arguments.

Received: November 6, 2010

AMS Subject Classification: 11N37, 11A25

Key Words and Phrases: perimeter, integral triangle, Eisenstein triple, lattice point

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 64
Issue: 4