All Questions

NB: this is a cross-posting from from MSE after two months with no progress (despite a bounty). It's totally elementary but I think it's cute. Consider the elliptic curve defined by the cubic: $$ a^...

Is there anything known about the existence of Heronian triangles ABC (i.e. with rational side lengths and rational area) that can be decomposed into three Heronian triangles ABD, BCD, CAD? ...

There is no Heronian triangle (or simply consider triangles on an integer lattice which also have integer side lengths) for which one side is half the length of another side. What other "side-side ...