On the generation of Heronian triangles

Abstract

We describe several algorithms for the generation of integer Heronian triangles with diameter at most n. Two of them have running time O n 2+ε . We enumerate all integer Heronian triangles for n ≤ 600000 and apply the complete list on some related problems.Lemma 2.1. We can assume that the denominator q can be written as q = w 1 w 2 w 3 w 4 with pairwise coprime integers w 1 , w 2 , w 3 , w 4 and

Errata and Addenda to Mathematical Constants

“…as n → ∞. The quantity H h (n) should be defined as the number of primitive Heronian triangles under the constraint that all three sides are ≤ n. A better starting point for studying H ′ a (n) might be [571,572,573,574]. 5.3.…”