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
“…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.…”
Section: Abelian Group Enumeration Constants Asymptotic Expansions Formentioning
We humbly and briefly offer corrections and supplements to Mathematical Constants (2003) and Mathematical Constants II (2019), both published by Cambridge University Press. Comments are always welcome.
“…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.…”
Section: Abelian Group Enumeration Constants Asymptotic Expansions Formentioning
We humbly and briefly offer corrections and supplements to Mathematical Constants (2003) and Mathematical Constants II (2019), both published by Cambridge University Press. Comments are always welcome.
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