Somos defines a rational triangle as a triangle such that all three sides measured relative to each other are rational. Koblitz defined a congruent number as an integer that is equal to the area of a rational right triangle. The discovery that a right triangle of unit leg length has an irrational hypotenuse (having a length equal to a value now known as Pythagoras's constant) showed that not all triangles are rational. Conway and Guy define a rational triangle as a triangle all of whose sides are rational numbers and all of whose angles are rational numbers of degrees. The only such triangle is the equilateral triangle.

congruent number | equilateral triangle | Fermat's right triangle theorem | Heronian triangle | Pythagoras's constant | rational quadrilateral | right triangle