Heronian Triangles. I. Systematic relation among the isosceles Heronian triangles.

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  • Heronian triangles 1 Systematic relation among the isosceles Heronian triangles

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A Heronian triangle (HeT) is defined here to be a triangle whose edges and area Δ are integers. A HeT (a, a, b) with coprime a and b is called a primitive isosceles Heronian triangle (piHeT). All the piHeT's are shown to be classified into two groups, I and II, depending on the value of 2a-b, and a pair of natural numbers, (n, k), called "family register codes", are shown to generate a pair of piHeT each belonging to I and II, together with a limited number of non-primitive triangles. However, by including those non-primitive members the a, b, and Δ values of all the family members of piHeT are uniquely generated and related with each other through simple recursion formulas.

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