Exact Formula For Heronian Triangles
All Heronian triangles can be generated as multiples of:
for integers m, n and k where:
- .
For example, taking m = 36, n = 4 and k = 3 produces a triangle with a = 5220, b = 900 and c = 5400, which is similar to the 5, 29, 30 Heronian triangle.
See also Heronian triangles with one angle equal to twice another.
Read more about this topic: Heronian Triangle
Famous quotes containing the words exact, formula and/or triangles:
“I think that cars today are almost the exact equivalent of the great Gothic cathedrals: I mean the supreme creation of an era, conceived with passion by unknown artists, and consumed in image if not in usage by a whole population which appropriates them as a purely magical object.”
—Roland Barthes (19151980)
“Ideals possess the strange quality that if they were completely realized they would turn into nonsense. One could easily follow a commandment such as Thou shalt not kill to the point of dying of starvation; and I might establish the formula that for the proper functioning of the mesh of our ideals, as in the case of a strainer, the holes are just as important as the mesh.”
—Robert Musil (18801942)
“If triangles had a god, they would give him three sides.”
—Charles Louis de Secondat Montesquieu (16891755)