Definition:Heronian Triangle
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Definition
Definition 1
A Heronian triangle is a triangle whose side lengths and area are all rational numbers.
Definition 2
A Heronian triangle is a triangle whose side lengths and altitudes are all rational numbers.
Also known as
Some sources do not use a capital H: heronian triangle.
Some sources refer to a Heronian triangle as a rational triangle.
Also see
- Results about Heronian triangles can be found here.
Source of Name
This entry was named for Heron of Alexandria.
Historical Note
In his Diophanti Alexandrini Arithmeticorum of $1621$, Claude Bachet raises the question of Heronian triangles in a commentary on Problem $18$ of Book $\text {VI}$.