A Formula for the Evans Triangle

by Open Science Repository Mathematics
(September 2013)

Abstract

In 1977, R. J. Evans posed a question in the American Mathematical Monthly: find every triangle with integer sides in which the altitude to the base divides that base in an integer ratio. He showed that the only such triangle has d = 3, and he gave an example with side lengths 3, 8 and 53. In 2009, Hin constructed a family of such triangles and demonstrated that infinitely many exist. This paper presents a formula derived from Evans' definition of the triangle, and uses it to obtain Evans triangles.

Keywords: integers, rational numbers.

Full text

A Formula for the Evans Triangle