Heronian triangle [SEP] named after
Heronian triangle
In geometry, a Heronian triangle is a triangle that has side lengths and area that are all integers. Heronian triangles are named after Hero of Alexandria. The term is sometimes applied more widely to triangles whose sides and area are all rational numbers, since one can rescale the sides by a common multiple to obtain a triangle that is Heronian in the above sense.
Properties.
Any right-angled triangle whose sidelengths are a Pythagorean triple is a Heronian triangle, as the side lengths of such a triangle
distance between the incenter and the circumcenter of an integer triangle, given by Euler's theorem as "R−2Rr", is rational.
Heronian triangles.
All Heronian triangles can be placed on a lattice with each vertex at a lattice point.
Heronian triangles General formula.
A Heronian triangle, also known as a Heron triangle or a Hero triangle, is a triangle with integer sides and integer area. Every Heronian triangle has sides proportional to
for integers "m", "n" and "k" subject