A223941 Areas of primitive Heron triangles with two rational triangle medians.
420, 55440, 2042040, 23931600, 75698280, 142334216640, 1877686881840, 185643608470320, 2137147184560080
Offset: 1
Links
- Ralph H. Buchholz and Randall L. Rathbun, An infinite set of Heron triangles with two rational medians, The American Mathematical Monthly, Vol. 104, No. 2 (Feb., 1997), pp. 107-115.
- Andrew N. W. Hone, Heron Triangles and the Hunt for Unicorns, Math. Intelligencer (2024); arXiv:2401.05581 [math.NT], 2024.
- Eric Weisstein's World of Mathematics, Heronian Triangle
Programs
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Mathematica
(*Brute-force search*)lst = {}; Do[s = (a + b + c)/2; d = Sqrt[s*(s - a)*(s - b)*(s - c)]; If[IntegerQ[d] && Divisible[d, 30] && d > 0, p = {{a, c, b}, {b, c, a}}; t = 0; Do[m = 1/2*Sqrt[2*p[[n, 1]]^2 + 2*p[[n, 2]]^2 - p[[n, 3]]^2]; If[MatchQ[m, _Rational] || IntegerQ[m], t++, Break[]], {n, 2}]; If[t == 2, AppendTo[lst, d]]], {a, 73}, {b, 51}, {c, 26}]; lst
Extensions
a(7)-a(9) from Hone (2024) added by Andrey Zabolotskiy, Apr 06 2024
Comments